## Publications

425 results found

Skrzypek T, Tseytlin AA, 2022, On type 0 string theory in solvable RR backgrounds, Publisher: ArXiv

Motivated by a possibility of solving non-supersymmetric type 0 string theoryin $AdS_5 \times S^5$ background using integrability, we revisit theconstruction of type 0 string spectrum in some solvable examples of backgroundswith RR fluxes that are common to type IIB and type 0B theories. The presenceof RR fluxes requires the use of a Green-Schwarz description for type 0 stringtheory. Like in flat space, the spectrum of type 0 theory can be derived fromthe type II theory spectrum by a $(-1)^F$ orbifolding, i.e. combining theuntwisted sector where GS fermions are periodic with the twisted sector whereGS fermions are antiperiodic (and projecting out all spacetime fermionicstates). This construction of the type 0 spectrum may also be implemented usinga Melvin background that allows to continuously interpolate between the type IIand type 0 theories. As an illustration, we discuss the type 0B spectrum in thepp-wave background which is the Penrose limit of $AdS_5 \times S^5$ with RR5-form flux and also in the pp-wave background which is the Penrose limit of$AdS_3 \times S^3 \times T^4$ supported by mixed RR and NSNS 3-form fluxes. Weshow that increasing the strength of the RR flux increases the value of theeffective normal ordering constant (which determines the mass of the type 0tachyon) and thus effectively decreases the momentum-space domain ofinstability of the ground state. We also comment on the semiclassical sector ofstates of type 0B theory in $AdS_5 \times S^5$.

Beccaria M, Giombi S, Tseytlin A, 2022, Wilson loop in general representation and RG flow in 1d defect QFT

The generalized Wilson loop operator interpolating between the supersymmetric and the ordinary Wilson loop in N=4 SYM theory provides an interesting example of renormalization group flow on a line defect: the scalar coupling parameter ζ has a non-trivial beta function and may be viewed as a running coupling constant in a 1d defect QFT. In this paper we continue the study of this operator, generalizing previous results for the beta function and Wilson loop expectation value to the case of an arbitrary representation of the gauge group and beyond the planar limit. Focusing on the scalar ladder limit where the generalized Wilson loop reduces to a purely scalar line operator in a free adjoint theory, and specializing to the case of the rank k symmetric representation of SU(N), we also consider a certain semiclassical limit where k is taken to infinity with the product kζ2 fixed. This limit can be conveniently studied using a 1d defect QFT representation in terms of N commuting bosons. Using this representation, we compute the beta function and the circular loop expectation value in the large k limit, and use it to derive constraints on the structure of the beta function for general representation. We discuss the corresponding 1d RG flow and comment on the consistency of the results with the 1d defect version of the F-theorem.

Beccaria M, Tseytlin AA, 2022, 1/N expansion of circular Wilson loop in N = 2 superconformal SU(N) x SU(N) quiver (vol 265, JHEP04, 2021), *The Journal of High Energy Physics*, Vol: 115, ISSN: 1029-8479

Beccaria M, Giombi S, Tseytlin AA, 2022, Higher order RG flow on the Wilson line in N=4 SYM, *The Journal of High Energy Physics*, Vol: 2022, Pages: 1-28, ISSN: 1029-8479

Extending earlier work, we find the two-loop term in the beta-function for the scalar coupling ζ in a generalized Wilson loop operator of the N = 4 SYM theory, working in the planar weak-coupling expansion. The beta-function for ζ has fixed points at ζ = ±1 and ζ = 0, corresponding respectively to the supersymmetric Wilson-Maldacena loop and to the standard Wilson loop without scalar coupling. As a consequence of our result for the beta-function, we obtain a prediction for the two-loop term in the anomalous dimension of the scalar field inserted on the standard Wilson loop. We also find a subset of higher-loop contributions (with highest powers of ζ at each order in ‘t Hooft coupling λ) coming from the scalar ladder graphs determining the corresponding terms in the five-loop beta-function. We discuss the related structure of the circular Wilson loop expectation value commenting, in particular, on consistency with a 1d defect version of the F-theorem. We also compute (to two loops in the planar ladder model approximation) the two-point correlators of scalars inserted on the Wilson line

Beccaria M, Dunne G, Tseytlin AA, 2021, Strong coupling expansion of free energy and BPS Wilson loop in N=2 superconformal models with fundamental hypermultiplets, *The Journal of High Energy Physics*, Vol: 2021, Pages: 1-42, ISSN: 1029-8479

As a continuation of the study (in arXiv:2102.07696 and arXiv:2104.12625) of strong-coupling expansion of non-planar corrections in N = 2 4d superconformal models we consider two special theories with gauge groups SU(N) and Sp(2N). They contain N-independent numbers of hypermultiplets in rank 2 antisymmetric and fundamental representations and are planar-equivalent to the corresponding N = 4 SYM theories. These N = 2 theories can be realised on a system of N D3-branes with a finite number of D7-branes and O7-plane; the dual string theories should be particular orientifolds of AdS5 × S5 superstring. Starting with the localization matrix model representation for the N = 2 partition function on S4 we find exact differential relations between the 1/N terms in the corresponding free energy F and the 12-BPS Wilson loop expectation value ⟨W⟩ and also compute their large ’t Hooft coupling (λ » 1) expansions. The structure of these expansions is different from the previously studied models without fundamental hypermultiplets. In the more tractable Sp(2N) case we find an exact resummed expression for the leading strong coupling terms at each order in the 1/N expansion. We also determine the exponentially suppressed at large λ contributions to the non-planar corrections to F and ⟨W⟩ and comment on their resurgence properties. We discuss dual string theory interpretation of these strong coupling expansions.Download to read the full article text

Beccaria M, Dunne G, Tseytlin AA, 2021, BPS Wilson loop in N=2 superconformal SU(N) "orientifold" gauge theory and weak-strong coupling interpolation, *The Journal of High Energy Physics*, Vol: 2021, Pages: 1-30, ISSN: 1029-8479

We consider the expectation value ⟨W⟩ of the circular BPS Wilson loop in N = 2 superconformal SU(N) gauge theory containing a vector multiplet coupled to two hypermultiplets in rank-2 symmetric and antisymmetric representations. This theory admits a regular large N expansion, is planar-equivalent to N = 4 SYM theory and is expected to be dual to a certain orbifold/orientifold projection of AdS5 × S5 superstring theory. On the string theory side ⟨W⟩ is represented by the path integral expanded near the same AdS2 minimal surface as in the maximally supersymmetric case. Following the string theory argument in [5], we suggest that as in the N = 4 SYM case and in the N = 2 SU(N) × SU(N) superconformal quiver theory discussed in [19], the coefficient of the leading non-planar 1/N2 correction in ⟨W⟩ should have the universal λ3/2 scaling at large ’t Hooft coupling. We confirm this prediction by starting with the localization matrix model representation for ⟨W⟩. We complement the analytic derivation of the λ3/2 scaling by a numerical high-precision resummation and extrapolation of the weak-coupling expansion using conformal mapping improved Padé analysis.

Levine N, Tseytlin AA, 2021, Integrability vs. RG flow in G x G and G x G/H sigma models, *The Journal of High Energy Physics*, Vol: 2021, Pages: 1-32, ISSN: 1029-8479

We consider a class of 2d σ-models on products of group spaces that provide new examples of a close connection between integrability and stability under the RG flow. We first study the integrable G × G model derived from the affine Gaudin construction (for which the 1-loop β-functions were found in arXiv:2010.07879) and show that its condition of integrability is preserved also by the 2-loop RG flow. We then investigate the RG flow in the gauged G × G/H model, in particular the integrable T1,1 model found in arXiv:2010.05573. We also construct a new class of integrable G × G/H models in the case when the subgroup H is abelian. In the simplest case of G = SU2, H = U1 this leads to an integrable σ-model on the T1,q space (with a particular B-field). This model is also shown to be stable under the 2-loop RG flow, and we relate this property to its invariance under T-duality in an isometric U1 direction. This T1,q model may be interpreted as an integrable deformation of the GMM model (of two coupled WZW theories with generic levels) away from the conformal point.

Beccaria M, Tseytlin AA, 2021, 1/N expansion of circular Wilson loop in N=2 superconformal SU(N) x SU(N) quiver, *The Journal of High Energy Physics*, Vol: 2021, Pages: 1-33, ISSN: 1029-8479

Localization approach to N = 2 superconformal SU(N) × SU(N) quiver theory leads to a non-Gaussian two-matrix model representation for the expectation value of BPS circular SU(N) Wilson loop ⟨W⟩. We study the subleading 1/N2 term in the large N expansion of ⟨W⟩ at weak and strong coupling. We concentrate on the case of the symmetric quiver with equal gauge couplings which is equivalent to the ℤ2 orbifold of the SU(2N) N = 4 SYM theory. This orbifold gauge theory should be dual to type IIB superstring in AdS5 × (S5/ℤ2). We present a string theory argument suggesting that the 1/N2 term in ⟨W⟩ in the orbifold theory should have the same strong-coupling asymptotics λ3/2 as in the N = 4 SYM case. We support this prediction on the gauge theory side by a numerical study of the localization matrix model. We also find a relation between the 1/N2 term in the Wilson loop expectation value and the derivative of the free energy of the orbifold gauge theory on 4-sphere.

Beccaria M, Tseytlin AA, 2021, On the structure of non-planar strong coupling corrections to correlators of BPS Wilson loops and chiral primary operators, *The Journal of High Energy Physics*, Vol: 2021, Pages: 1-47, ISSN: 1029-8479

Starting with some known localization (matrix model) representations for correlators involving 1/2 BPS circular Wilson loop W in N = 4 SYM theory we work out their 1/N expansions in the limit of large ’t Hooft coupling λ. Motivated by a possibility of eventual matching to higher genus corrections in dual string theory we follow arXiv:2007.08512 and express the result in terms of the string coupling gs∼g2YM∼λ/N and string tension T∼λ−−√. Keeping only the leading in 1/T term at each order in gs we observe that while the expansion of ⟨W⟩ is a series in g2s/T, the correlator of the Wilson loop with chiral primary operators OJ has expansion in powers of g2s/T2. Like in the case of ⟨W⟩ where these leading terms are known to resum into an exponential of a “one-handle” contribution ∼g2s/T, the leading strong coupling terms in ⟨WOJ⟩ sum up to a simple square root function of g2s/T2. Analogous expansions in powers of g2s/T are found for correlators of several coincident Wilson loops and they again have a simple resummed form. We also find similar expansions for correlators of coincident 1/2 BPS Wilson loops in the ABJM theory.

Hoare B, Levine N, Tseytlin AA, 2020, Sigma models with local couplings: a new integrability-RG flow connection, *The Journal of High Energy Physics*, Vol: 20, ISSN: 1029-8479

We consider several classes of σ-models (on groups and symmetric spaces, η-models, ⋋-models) with local couplings that may depend on the 2d coordinates, e.g. on time τ . We observe that (i) starting with a classically integrable 2d σ-model, (ii) formally promoting its couplings hα to functions hα(τ ) of 2d time, and (iii) demanding that the resulting time-dependent model also admits a Lax connection implies that hα(τ ) must solve the 1-loop RG equations of the original theory with τ interpreted as RG time. This provides a novel example of an ‘integrability-RG flow’ connection. The existence of a Lax connection suggests that these time-dependent σ-models may themselves be understood as integrable. We investigate this question by studying the possibility of constructing non-local and local conserved charges. Such σ-models with D-dimensional target space and time-dependent couplings subject to the RG flow naturally appear in string theory upon fixing the light-cone gauge in a (D + 2)-dimensional conformal σ-model with a metric admitting a covariantly constant null Killing vector and a dilaton linear in the null coordinate.

Giombi S, Tseytlin AA, 2020, Strong coupling expansion of circular Wilson loops and string theories in AdS5 x S^5 and AdS4 x CP^3, *The Journal of High Energy Physics*, Vol: 2020, Pages: 1-27, ISSN: 1029-8479

We revisit the problem of matching the strong coupling expansion of the$\frac{1}{2}$ BPS circular Wilson loops in ${\cal N}=4$ SYM and ABJM gaugetheories with their string theory duals in ${\rm AdS}_5 \times S^5$ and ${\rmAdS}_4 \times CP^3$, at the first subleading (one-loop) order of the expansionaround the minimal surface. We observe that, including the overall factor$1/g_{\rm s}$ of the inverse string coupling constant, as appropriate for theopen string partition function with disk topology, and a universal prefactorproportional to the square root of the string tension $T$, both the SYM andABJM results precisely match the string theory prediction. We provide anexplanation of the origin of the $\sqrt T$ prefactor based on special featuresof the combination of one-loop determinants appearing in the string partitionfunction. The latter also implies a natural generalization $Z_\chi \sim (\sqrtT/g_{\rm s})^\chi$ to higher genus contributions with the Euler number $\chi$,which is consistent with the structure of the $1/N$ corrections found on thegauge theory side.

Pasarin O, Tseytlin AA, 2020, Generalised Schwarzschild metric from double copy of point-like charge solution in Born-Infeld theory, *Physics Letters B*, Vol: 807, Pages: 1-6, ISSN: 0370-2693

We discuss possible application of the classical double copy procedure to construction of a generalisation of the Schwarzschild metric starting from an -corrected open string analogue of the Coulomb solution. The latter is approximated by a point-like charge solution of the Born-Infeld action, which represents the open string effective action for an abelian vector field in the limit when derivatives of the field strength are small. The Born-Infeld solution has a regular electric field which is constant near the origin suggesting that corrections from the derivative terms in the open string effective action may be small there. The generalization of the Schwarschild metric obtained by the double copy construction from the Born-Infeld solution looks non-singular but the corresponding curvature invariants still blow up at . We discuss the origin of this singularity and comment on possible generalizations.

Drukker N, Giombi S, Tseytlin AA,
et al., 2020, Defect CFT in the 6d (2,0) theory from M2 brane dynamics in AdS7×S4, *The Journal of High Energy Physics*, Vol: 2020, ISSN: 1029-8479

Surface operators in the 6d (2,0) theory at large $N$ have a holographicdescription in terms of M2 branes probing the AdS$_7 \times S^4$ M-theorybackground. The most symmetric, 1/2-BPS, operator is defined over a planar orspherical surface, and it preserves a 2d superconformal group. This includes,in particular, an $SO(2,2)$ subgroup of 2d conformal transformations, so thatthe surface operator may be viewed as a conformal defect in the 6d theory. Thedual M2 brane has an AdS$_3$ induced geometry, reflecting the 2d conformalsymmetry. Here we use the holographic description to extract the defect CFTdata associated to the surface operator. The spectrum of transversefluctuations of the M2 brane is found to be in one-to-one correspondence with aprotected multiplet of operator insertions on the surface, which includes thedisplacement operator. We compute the one-loop determinants of fluctuations ofthe M2 brane, and extract the conformal anomaly coefficient of the sphericalsurface to order $N^0$. We also briefly discuss the RG flow from thenon-supersymmetric to the 1/2-BPS defect operator, and its consistency with a"$b$-theorem" for the defect CFT. Starting with the M2 brane action, we thenuse AdS$_3$ Witten diagrams to compute the 4-point functions of the elementarybosonic insertions on the surface operator, and extract some of the defect CFTdata from the OPE. The 4-point function is shown to satisfy superconformal Wardidentities, and we discuss a related subsector of "twisted" scalar insertions,whose correlation functions are constrained by the residual superconformalsymmetry.

Beccaria M, Jiang H, Tseytlin AA, 2020, Boundary correlators in WZW model on AdS2, *The Journal of High Energy Physics*, Vol: 2020, Pages: 1-37, ISSN: 1029-8479

Boundary correlators of elementary fields in some 2d conformal field theories defined on AdS2 have a particularly simple structure. For example, the correlators of the Liouville scalar happen to be the same as the correlators of the chiral component of the stress tensor on a plane restricted to the real line. Here we show that an analogous relation is true also in the WZW model: boundary correlators of the WZW scalars have the same structure as the correlators of chiral Kac-Moody currents. This is checked at the level of the tree and one-loop Witten diagrams in AdS2. We also compute some tree-level correlators in a generic σ-model defined on AdS2 and show that they simplify only in the WZW case where an extra Kac-Moody symmetry appears. In particular, the terms in 4- point correlators having logarithmic dependence on 1d cross-ratio cancel only at the WZW point. One motivation behind this work is to learn how to compute AdS2 loop corrections in 2d models with derivative interactions related to the study of correlators of operators on Wilson loops in string theory in AdS.

Tseytlin AA, 2020, Comments on open string with 'massive' boundary term, *Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences*, Vol: 476, Pages: 1-9, ISSN: 1364-5021

We discuss possible definition of open string path integral in the presence of additional boundary couplings corresponding to the presence of masses at the ends of the string. These couplings are not conformally invariant implying that as in a non-critical string case one is to integrate over the one-dimensional metric or reparametrizations of the boundary. We compute the partition function on the disc in the presence of an additional constant gauge field background and comment on the structure of the corresponding scattering amplitudes.

Hoare B, Levine N, Tseytlin AA, 2019, Integrable sigma models and 2-loop RG flow, *The Journal of High Energy Physics*, Vol: 2019, Pages: 1-32, ISSN: 1029-8479

Following arXiv:1907.04737, we continue our investigation of the relation between the renormalizability (with finitely many couplings) and integrability in 2d σ- models. We focus on the “λ-model,” an integrable model associated to a group or symmetric space and containing as special limits a (gauged) WZW model and an “interpolating model” for non-abelian duality. The parameters are the WZ level k and the coupling λ, and the fields are g, valued in a group G, and a 2d vector A± in the corresponding algebra. We formulate the λ-model as a σ-model on an extended G × G × G configuration space (g, h,h¯¯¯), defining h and h¯¯¯ by A+ = h∂+h−1, A_ = h¯¯¯∂−h¯¯¯−1. Our central observation is that the model on this extended configuration space is renormalizable without any deformation, with only λ running. This is in contrast to the standard σ-model found by integrating out A±, whose 2-loop renormalizability is only obtained after the addition of specific finite local counterterms, resulting in a quantum deformation of the target space geometry. We compute the 2-loop β-function of the λ-model for general group and symmetric spaces, and illustrate our results on the examples of SU(2)/U(1) and SU(2). Similar conclusions apply in the non-abelian dual limit implying that non-abelian duality commutes with the RG flow. We also find the 2-loop β-function of a “squashed” principal chiral model.

Hoare B, Levine N, Tseytlin AA, 2019, Integrable 2d sigma models: Quantum corrections to geometry from RG flow, *Nuclear Physics B*, Vol: 949, Pages: 1-17, ISSN: 0550-3213

Classically integrable σ-models are known to be solutions of the 1-loop RG equations, or “Ricci flow”, with only a few couplings running. In some of the simplest examples of integrable deformations we find that in order to preserve this property at 2 (and higher) loops the classical σ-model should be corrected by quantum counterterms. The pattern is similar to that of effective σ-models associated to gauged WZW theories. We consider in detail the examples of the η-deformation of S2 (“sausage model”) and H2 , as well as the closely related λ-deformation of the SO (1,2)/SO(2) coset. We also point out that similar counterterms are required in order for non-abelian duality to commute with RG flow beyond the 1-loop order.

Beccaria M, Jiang H, Tseytlin AA, 2019, Supersymmetric Liouville theory in AdS(2) and AdS/CFT, *The Journal of High Energy Physics*, Vol: 2019, Pages: 1-44, ISSN: 1029-8479

In a series of recent papers, a special kind of AdS2/CFT1 duality was observed: the boundary correlators of elementary fields that appear in the Lagrangian of a 2d conformal theory in rigid AdS2 background are the same as the correlators of the corresponding primary operators in the chiral half of that 2d CFT in flat space restricted to the real line. The examples considered were: (i) the Liouville theory where the operator dual to the Liouville scalar in AdS2 is the stress tensor; (ii) the abelian Toda theory where the operators dual to the Toda scalars are the W -algebra generators; (iii) the non-abelian Toda theory where the Liouville field is dual to the stress tensor while the extra gauged WZW theory scalars are dual to non-abelian parafermionic operators. By direct Witten diagram com- putations in AdS2 one can check that the structure of the boundary correlators is indeed consistent with the Virasoro (or higher) symmetry. Here we consider a supersymmetric generalization: the N = 1 superconformal Liouville theory in AdS2. We start with the super Liouville theory coupled to 2d supergravity and show that a consistent restriction to rigid AdS2 background requires a non-zero value of the supergravity auxiliary field and thus a modification of the Liouville potential from its familiar flat-space form. We show that the Liouville scalar and its fermionic partner are dual to the chiral half of the stress tensor and the supercurrent of the super Liouville theory on the plane. We perform tests supporting the duality by explicitly computing AdS2 Witten diagrams with bosonic and fermionic loops.

Beccaria M, Jiang H, Tseytlin AA, 2019, Non-abelian Toda theory on AdS(2) and AdS(2)/CFT21/2 duality, *The Journal of High Energy Physics*, Vol: 36, Pages: 1-42, ISSN: 1029-8479

It was recently observed that boundary correlators of the elementary scalar field of the Liouville theory on AdS2 background are the same (up to a non-trivial proportionality coefficient) as the correlators of the chiral stress tensor of the Liouville CFT on the complex plane restricted to the real line. The same relation generalizes to the conformal abelian Toda theory: boundary correlators of Toda scalars on AdS2 are directly related to the correlation functions of the chiral -symmetry generators in the Toda CFT and thus are essentially controlled by the underlying infinite-dimensional symmetry. These may be viewed as examples of AdS2/CFT1 duality where the CFT1 is the chiral half of a 2d CFT; we shall to this as AdS2/CFT1/22 . In this paper we demonstrate that this duality applies also to the non-abelian Toda theory containing a Liouville scalar coupled to a 2d σ-model originating from the SL(2, ℝ)/U(1) gauged WZW model. Here the Liouville scalar is again dual to the chiral stress tensor T while the other two scalars are dual to the parafermionic operators V± of the non-abelian Toda CFT. We explicitly check the duality at the next-to-leading order in the large central charge expansion by matching the chiral CFT correlators of (T, V+, V−) (computed using a free field representation) with the boundary correlators of the three Toda scalars given by the tree-level and one-loop Witten diagrams in AdS2.

Casarin L, Tseytlin AA, 2019, One-loop beta-functions in 4-derivative gauge theory in 6 dimensions, *The Journal of High Energy Physics*, Vol: 159, Pages: 1-18, ISSN: 1029-8479

A classically scale-invariant 6d analog of the 4d Yang-Mills theory is the 4-derivative (∇F )2 + F 3 gauge theory with two independent couplings. Motivated by a search for a perturbatively conformal but possibly non-unitary 6d models we compute the one-loop β-functions in this theory. A systematic way of doing this using the back-ground field method requires the (previously unknown) expression for the b6 Seeley-DeWitt coefficient for a generic 4-derivative operator; we derive it here. As an application, we also compute the one-loop β-function in the (1,0) supersymmetric (∇F )2 6d gauge theory con-structed in hep-th/0505082.

Beccaria M, Tseytlin AA, 2019, On boundary correlators in Liouville theory on AdS(2), *Journal of High Energy Physics*, Vol: 2019, Pages: 1-26, ISSN: 1029-8479

We consider the Liouville theory in fixed Euclidean AdS2 background. Expanded near the minimum of the potential the elementary field has mass squared 2 and (assuming the standard Dirichlet b.c.) corresponds to a dimension 2 operator at the boundary. We provide strong evidence for the conjecture that the boundary correlators of the Liouville field are the same as the correlators of the holomorphic stress tensor (or the Virasoro generator with the same central charge) on a half-plane or a disc restricted to the boundary. This relation was first observed at the leading semiclassical order (tree-level Witten diagrams in AdS2) in [19] and here we demonstrate its validity also at the one-loop level. We also discuss arguments that may lead to its general proof.

Beccaria M, Giombi S, Tseytlin AA, 2019, Correlators on non-supersymmetric Wilson line in N=4 SYM and AdS(2)/CFT1, *Journal of High Energy Physics*, Vol: 122, Pages: 1-61, ISSN: 1029-8479

Correlators of local operators inserted on a straight or circular Wilson loop in a conformal gauge theory have the structure of a one-dimensional “defect” CFT. As was shown in arXiv:1706.00756, in the case of supersymmetric Wilson-Maldacena loop in N=4 SYM one can compute the leading strong-coupling contributions to 4-point correlators of the simplest “protected” operators by starting with the AdS5 × S5 string action expanded near the AdS2 minimal surface and evaluating the corresponding tree-level AdS2 Witten diagrams. Here we perform the analogous computations in the non-supersymmetric case of the standard Wilson loop with no coupling to the scalars. The corresponding non-supersymmetric “defect” CFT1 should have an unbroken SO(6) global symmetry. The elementary bosonic operators (6 SYM scalars and 3 components of the SYM field strength) are dual respectively to the S5 embedding coordinates and AdS5 coordinates transverse to the minimal surface ending on the line at the boundary. The SO(6) symmetry is preserved on the string side provided the 5-sphere coordinates satisfy Neumann boundary conditions (as opposed to Dirichlet in the supersymmetric case); this implies that one should integrate over the S5 expansion point. The massless S5 fluctuations then have logarithmic propagator, corresponding to the boundary scalar operator having dimension Δ=5λ√+… at strong coupling. The resulting functions of 1d cross-ratio appearing in the 4-point functions turn out to have a more complicated structure than in the supersymmetric case, involving polylog (Li3 and Li2) functions. We also discuss consistency with the operator product expansion which allows extracting the leading strong coupling corrections to the anomalous dimensions of the operators appearing in the intermediate channels.

Hoare B, Levine N, Tseytlin AA, 2019, On the massless tree-level S-matrix in 2d sigma models, *Journal of Physics A: Mathematical and Theoretical*, ISSN: 1751-8113

Beccaria M, Tseytlin AA, 2018, Superconformal index of higher derivative N=1 multiplets in four dimensions, *JOURNAL OF HIGH ENERGY PHYSICS*, Vol: 2018, ISSN: 1029-8479

Supersymmetric partition function of N=1 superconformal theories on S β 1 × S3 is related to the superconformal index receiving contributions from short representations. The leading coefficients in the small β (high “temperature”) expansion of the index were previously related to the conformal anomaly coefficients of the theory. Assumptions underlying universality of these relations were tested only for simplest low-spin unitary multiplets. Here we consider examples of higher derivative non-unitary N=1 multiplets that naturally appear in the context of extended conformal supergravities and compute their superconformal index. We compare the coefficients in the small β expansion of the index with those proposed earlier for unitary multiplets and suggest some modifications that should apply universally to all types of theories. We also comment on the structure of subleading terms and the case of N=4 conformal supergravity.

Beccaria M, Tseytlin AA, 2018, On non-supersymmetric generalizations of the Wilson-Maldacena loops in N=4 SYM, *Nuclear Physics B*, Vol: 934, Pages: 466-497, ISSN: 0550-3213

Building on our previous work arXiv:1712.06874 we consider one-parameter Polchinski–Sully generalization of the Wilson–Maldacena (WM) loops in planar SYM theory. This breaks local supersymmetry of WM loop and leads to running of the deformation parameter ζ. At three-loop level, we compute the ladder diagram contribution to the expectation value of the circular loop which is dominant for large ζ. The limit fixed in which the expectation value is determined by the Gaussian adjoint scalar path integral might be exactly solvable despite the lack of global supersymmetry. We study similar generalization of the -BPS “latitude” WM loop which depends on two parameters (in addition to the 't Hooft coupling λ). One may also introduce another supersymmetry-breaking parameter – the winding number of the scalar coupling circle. We find the two-loop expression for the expectation value of the associated loop by combining the ladder diagram contribution with an indirect determination of the non-ladder contribution using 1d defect CFT perturbation theory.

Adamo T, Nakach S, Tseytlin AA, 2018, Scattering of conformal higher spin fields, *Journal of High Energy Physics*, Vol: 2018, ISSN: 1029-8479

We develop a formalism for describing the most general notion of tree-level scattering amplitudes in 4d conformal higher spin theory. As conformal higher spin fields obey higher-derivative equations of motion, there are many distinct on-shell external states which may contribute to their scattering, some of which grow polynomially with time, leading to ill-defined amplitudes. We characterize the set of admissible scattering states which produce finite tree amplitudes, noting that there are more such states than just standard massless higher spins obeying two-derivative equations of motion. We use conformal gravity as a prime example, where the set of scattering states includes the usual Einstein graviton and a ‘ghost’ massless spin 1 particle. An extension of the usual spinor helicity formalism allows us to encode these scattering states efficiently in terms of ‘twistor-spinors’. This leads to compact momentum space expressions for all finite tree-level 3-point amplitudes of conformal higher spin theory. While some of these 3-point amplitudes vanish (including all those with only standard two-derivative higher spin external states), there are many others which are non-vanishing. We also comment on the generalization to scattering of conformal higher spins in AdS4.

Huang K-W, Roiban R, Tseytlin AA, 2018, Self-dual 6d 2-form fields coupled to non-abelian gauge field: quantum corrections, *JOURNAL OF HIGH ENERGY PHYSICS*, Vol: 2018, ISSN: 1029-8479

We study a 6d model of a set of self-dual 2-form B-fields interacting with a non-abelian vector A-field which is restricted to a 5d subspace. One motivation is that if the gauge vector could be expressed in terms of the B-field or integrated out, this model could lead to an interacting theory of B-fields only. Treating the 5d gauge vector as a background field, we compute the divergent part of the corresponding one-loop effective action which has the (DF)2 + F3 structure and compare it with similar contributions from other 6d fields. We also discuss a 4d analog of the non-abelian self-dual model, which turns out to be UV finite.

Medina-Rincon D, Tseytlin AA, Zarembo K, 2018, Precision matching of circular Wilson loops and strings in AdS₅ x S⁵, *Journal of High Energy Physics*, Vol: 2018, ISSN: 1029-8479

Previous attempts to match the exact N=4 super Yang-Mills expression for the expectation value of the 12 -BPS circular Wilson loop with the semiclassical AdS5 × S5 string theory prediction were not successful at the first subleading order. There was a missing prefactor ∼ λ−3/4 which could be attributed to the unknown normalization of the string path integral measure. Here we resolve this problem by computing the ratio of the string partition functions corresponding to the circular Wilson loop and the special 14 supersymmetric latitude Wilson loop. The fact that the latter has a trivial expectation value in the gauge theory allows us to relate the prefactor to the contribution of the three zero modes of the “transverse” fluctuation operator in the 5-sphere directions.

Beccaria M, Giombi S, Tseytlin AA, 2018, Non-supersymmetric Wilson loop in N=4 SYM and defect 1d CFT, *Journal of High Energy Physics*, Vol: 2018, ISSN: 1029-8479

Following Polchinski and Sully (arXiv:1104.5077), we consider a generalized Wilson loop operator containing a constant parameter ζ in front of the scalar coupling term, so that ζ = 0 corresponds to the standard Wilson loop, while ζ = 1 to the locally supersymmetric one. We compute the expectation value of this operator for circular loop as a function of ζ to second order in the planar weak coupling expansion in = 4 SYM theory. We then explain the relation of the expansion near the two conformal points ζ = 0 and ζ = 1 to the correlators of scalar operators inserted on the loop. We also discuss the AdS5 × S5 string 1-loop correction to the strong-coupling expansion of the standard circular Wilson loop, as well as its generalization to the case of mixed boundary conditions on the five-sphere coordinates, corresponding to general ζ. From the point of view of the defect CFT1 defined on the Wilson line, the ζ-dependent term can be seen as a perturbation driving a RG flow from the standard Wilson loop in the UV to the supersymmetric Wilson loop in the IR. Both at weak and strong coupling we find that the logarithm of the expectation value of the standard Wilson loop for the circular contour is larger than that of the supersymmetric one, which appears to be in agreement with the 1d analog of the F-theorem.

Tseytlin AA, 2017, On divergences in non-minimal N=4 conformal supergravity, *Journal of Physics A: Mathematical and Theoretical*, Vol: 50, ISSN: 1751-8113

We review the question of quantum consistency of $ \newcommand{\N}{{{\mathcal N}}} \N=4$ conformal supergravity in 4 dimensions. The UV divergences and anomalies of the standard ('minimal') conformal supergravity where the complex scalar $ \newcommand{\vp}{\varphi} \vp$ is not coupled to the Weyl graviton kinetic term can be cancelled by coupling this theory to $ \newcommand{\N}{{{\mathcal N}}} \N=4$ super Yang–Mills with gauge group of dimension 4. The same turns out to be true also for the 'non-minimal' $ \newcommand{\N}{{{\mathcal N}}} \N=4$ conformal supergravity with the action (recently constructed (Butter et al 2017 Phys. Rev. Lett. 118 081602)) depending on an arbitrary holomorphic function $ \newcommand{\vp}{\varphi} f(\vp)$ . The special case of the 'non-minimal' conformal supergravity with $ \newcommand{\vp}{\varphi} f= {\rm e}^{2\vp}$ appears in the twistor-string theory. We show that divergences and anomalies do not depend on the form of the function f and thus can be cancelled just as in the 'minimal' $f=1$ case by coupling the theory to four $ \newcommand{\N}{{{\mathcal N}}} \N=4$ vector multiplets.

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