Publications
438 results found
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.
Beccaria M, Tseytlin AA, 2017, C-T for conformal higher spin fields from partition function on conically deformed sphere, Journal of High Energy Physics, Vol: 2017, ISSN: 1029-8479
We consider the one-parameter generalization Sq4 of 4-sphere with a conical singularity due to identification τ = τ +2πq in one isometric angle. We compute the value of the spectral zeta-function at zero ζˆ(q)=ζ(0;q)ζ^(q)=ζ(0;q) that controls the coefficient of the logarithmic UV divergence of the one-loop partition function on Sq4. While the value of the conformal anomaly a-coefficient is proportional to ζˆ(1)ζ^(1), we argue that in general the second c ∼ CT anomaly coefficient is related to a particular combination of the second and first derivatives of ζˆ(q)ζ^(q) at q = 1. The universality of this relation for CT is supported also by examples in 6 and 2 dimensions. We use it to compute the c-coefficient for conformal higher spins finding that it coincides with the “r = −1” value of the one-parameter Ansatz suggested in arXiv:1309.0785. Like the sums of as and cs coefficients, the regularized sum of ζˆs(q)ζ^s(q) over the whole tower of conformal higher spins s = 1, 2,… is found to vanish, implying UV finiteness on Sq4 and thus also the vanishing of the associated Rényi entropy. Similar conclusions are found to apply to the standard 2-derivative massless higher spin tower. We also present an independent computation of the full set of conformal anomaly coefficients of the 6d Weyl graviton theory defined by a particular combination of the three 6d Weyl invariants that has a (2, 0) supersymmetric extension.
Giombia S, Roiban R, Tseytlin AA, 2017, Half-BPS Wilson loop and AdS(2)/CFT1, Nuclear Physics B, Vol: 922, Pages: 499-527, ISSN: 0550-3213
We study correlation functions of local operator insertions on the 1/2-BPS Wilson line in super Yang–Mills theory. These correlation functions are constrained by the 1d superconformal symmetry preserved by the 1/2-BPS Wilson line and define a defect CFT1 living on the line. At strong coupling, a set of elementary operator insertions with protected scaling dimensions correspond to fluctuations of the dual fundamental string in AdS ending on the line at the boundary and can be thought of as light fields propagating on the AdS2 worldsheet. We use AdS/CFT techniques to compute the tree-level AdS2 Witten diagrams describing the strong coupling limit of the four-point functions of the dual operator insertions. Using the OPE, we also extract the leading strong coupling corrections to the anomalous dimensions of the “two-particle” operators built out of elementary excitations. In the case of the circular Wilson loop, we match our results for the 4-point functions of a special type of scalar insertions to the prediction of localization to 2d Yang–Mills theory.
Beccaria M, Tseytlin AA, 2017, C-T for higher derivative conformal fields and anomalies of (1,0) superconformal 6d theories, JOURNAL OF HIGH ENERGY PHYSICS, Vol: 2017, ISSN: 1029-8479
In [8] we proposed the linear relations between the Weyl anomaly c1, c2, c3 coefficients and the 4 coefficients in the chiral anomaly polynomial for (1,0) superconformal 6d theories. These relations were determined up to one free parameter ξ and its value was then conjectured using some additional assumptions. A different value for ξ was recently suggested in arXiv:1702.03518 using an alternative method. Here we confirm that this latter value is indeed the correct one by providing an additional data point: the Weyl anomaly coefficient c3 for the higher derivative (1,0) superconformal 6d vector multiplet. This multiplet contains the 4-derivative conformal gauge vector, 3-derivative fermion and 2-derivative scalar. We find the corresponding value of c3 which is proportional to the coefficient CT in the 2-point function of stress tensor using its relation to the first derivative of the Renyi entropy or the second derivative of the free energy on the product of thermal circle and 5d hyperbolic space. We present some general results of the computation of the Rényi entropy and CT from the partition function on S1 × ℍd − 1 for higher derivative conformal scalars, spinors and vectors in even dimensions. We also give an independent derivation of the conformal anomaly coefficients of the 6d higher derivative vector multiplet from the Seeley-DeWitt coefficients on an Einstein background.
Beccaria M, Tseytlin AA, 2017, Partition function of free conformal fields in 3-plet representation, Journal of High Energy Physics, Vol: 2017, ISSN: 1029-8479
Simplest examples of AdS/CFT duality correspond to free CFTs in d dimensions with fields in vector or adjoint representation of an internal symmetry group dual in the large N limit to a theory of massless or massless plus massive higher spins in AdS d+1. One may also study generalizations when conformal fields belong to higher dimensional representations, i.e. carry more than two internal symmetry indices. Here we consider the case of the 3-fundamental (“3-plet”) representation. One motivation is a conjectured connection to multiple M5-brane theory: heuristic arguments suggest that it may be related to an (interacting) CFT of 6d (2,0) tensor multiplets in 3-plet representation of large N symmetry group that has an AdS7 dual. We compute the singlet partition function Z on S 1 × S d−1 for a free field in 3-plet representation of U(N) and analyse its novel large N behaviour. The large N limit of the low temperature expansion of Z which is convergent in the vector and adjoint cases here is only asymptotic, reflecting the much faster growth of the number of singlet operators with dimension, indicating a phase transition at very low temperature. Indeed, while the critical temperatures in the vector (T c ∼ N γ , γ > 0) and adjoint (T c ∼ 1) cases are finite, we find that in the 3-plet case T c ∼ (log N)−1, i.e. it approaches zero at large N. We discuss some details of large N solution for the eigenvalue distribution. Similar conclusions apply to higher p-plet representations of U(N) or O(N) and also to the free p-tensor theories invariant under [U(N)] p or [O(N)] p with p ≥ 3.
Roiban R, Tseytlin AA, 2017, On four-point interactions in massless higher spin theory in flat space, JOURNAL OF HIGH ENERGY PHYSICS, Vol: 2017, ISSN: 1029-8479
We consider a minimal interacting theory of a single tower of spin j = 0, 2, 4,… massless Fronsdal fields in flat space with local Lorentz-covariant cubic interaction vertices. We address the question of constraints on possible quartic interaction vertices imposed by the condition of on-shell gauge invariance of the tree-level four-point scattering amplitudes involving three spin 0 and one spin j particle. We find that these constraints admit a local solution for quartic 000j interaction term in the action only for j = 2 and j = 4. We determine the non-local terms in four-vertices required in the j ≥ 6 case and suggest that these non-localities may be interpreted as a result of integrating out a tower of auxiliary ghost-like massless higher spin fields in an extended theory with a local action, up to possible higher-point interactions of the ghost fields. We also consider the conformal off-shell extension of the Einstein theory and show that the perturbative expansion of its action is the same as that of the non-local action resulting from integrating out the trace of the graviton field from the Einstein action. Motivated by this example, we conjecture the existence of a similar conformal off-shell extension of a massless higher spin theory that may be related to the above extended theory. It may then have the same infinite-dimensional symmetry as the higher-derivative conformal higher spin theory and may thus lead to a trivial S matrix.
Beccaria M, Tseytlin AA, 2017, On induced action for conformal higher spins in curved background, Nuclear Physics B, Vol: 919, Pages: 359-383, ISSN: 0550-3213
We continue the investigation of the structure of the action for a tower of conformal higher spin fields in non-trivial 4d background metric recently discussed in Grigoriev and Tseytlin (2016) [15]. The action is defined as an induced one from path integral of a conformal scalar field in curved background coupled to higher spin fields. We analyze in detail the dependence of the quadratic part of the induced action on the spin 1 and spin 3 fields, determining the presence of a curvature-dependent mixed spin 1–3 term. One consequence is that the pure spin 3 kinetic term cannot be gauge-invariant on its own beyond the leading term in small curvature expansion. We also compute the non-zero contribution of the 1–3 mixing term to the conformal anomaly c-coefficient. One is thus to determine all such mixing terms before addressing the question of possible vanishing of the total c-coefficient in the conformal higher spin theory.
Grigoriev M, Tseytlin AA, 2017, On conformal higher spins in curved background, Journal of Physics A: Mathematical and Theoretical, Vol: 50, ISSN: 1751-8113
We address the question of how to represent an interacting action for a tower of conformal higher spin fields in a form covariant with respect to a background metric. We use the background metric to define the star product which plays a central role in the definition of the corresponding gauge transformations. By analogy with the kinetic term in the 4-derivative Weyl gravity action expanded near an on-shell background one expects that the kinetic term in such an action should be gauge-invariant in a Bach-flat metric. We demonstrate this fact to first order in expansion in powers of the curvature of the background metric. This generalizes the result of arXiv:1404.7452 for spin 3 case to all conformal higher spins. We also comment on a possibility of extending this claim to terms quadratic in the curvature and discuss the appearance of background-dependent mixing terms in the quadratic part of the conformal higher spin action.
Forini V, Tseytlin AA, Vescovi E, 2017, Perturbative computation of string one-loop corrections to Wilson loop minimal surfaces in AdS(5) x S-5, Journal of High Energy Physics, Vol: 2017, ISSN: 1029-8479
We revisit the computation of the 1-loop string correction to the “latitude” minimal surface in AdS5 × S5 representing 1/4 BPS Wilson loop in planar N=4 SYM theory previously addressed in arXiv:1512.00841 and arXiv:1601.04708. We resolve the problem of matching with the subleading term in the strong coupling expansion of the exact gauge theory result (derived previously from localization) using a different method to compute determinants of 2d string fluctuation operators. We apply perturbation theory in a small parameter (angle of the latitude) corresponding to an expansion near the AdS2 minimal surface representing 1/2 BPS circular Wilson loop. This allows us to compute the corrections to the heat kernels and zeta-functions of the operators in terms of the known heat kernels on AdS2. We apply the same method also to two other examples of Wilson loop surfaces: generalized cusp and k-wound circle.
Tseytlin AA, 2017, Scattering Via Conformal Higher Spin Exchanges, International Workshop on Higher-Spin Gauge Theories, Publisher: WORLD SCIENTIFIC PUBL CO PTE LTD, Pages: 39-50
Hoare B, Tseytlin AA, 2016, Homogeneous Yang-Baxter deformations as non-abelian duals of the AdS(5) sigma-model, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 49, ISSN: 1751-8113
Beccaria M, Nakach S, Tseytlin AA, 2016, On triviality of S-matrix in conformal higher spin theory, Journal of High Energy Physics, Vol: 2016, ISSN: 1029-8479
We consider the conformal higher spin (CHS) theory in d = 4 that contains thes = 1 Maxwell vector, s = 2 Weyl graviton and their higher spin s = 3, 4, . . . counterpartswith higher-derivative s kinetic terms. The interacting action for such theory can befound as the coefficient of the logarithmically divergent part in the induced action forsources coupled to higher spin currents in a free complex scalar field model. We explicitlydetermine some cubic and quartic interaction vertices in the CHS action from scalar loopintegrals. We then compute the simplest tree-level 4-particle scattering amplitudes 11→11,22→22 and 11→22 and find that after summing up all the intermediate CHS exchanges theyvanish. This generalises the vanishing of the scattering amplitude for external conformalscalars interacting via the exchange of all CHS fields found earlier in arXiv:1512.08896.This vanishing should generalise to all scattering amplitudes in the CHS theory and asin the conformal scalar scattering case should be a consequence of the underlying infinitedimensional higher spin symmetry that extends the standard conformal symmetry.
Tseytlin AA, Wulff L, 2016, Kappa-symmetry of superstring sigma model and generalized 10d supergravity equations, Journal of High Energy Physics, Vol: 2016, ISSN: 1029-8479
We determine the constraints imposed on the 10d target superspace geometry by the requirement of classical kappa-symmetry of the Green-Schwarz superstring. In the type I case we find that the background must satisfy a generalization of type I supergravity equations. These equations depend on an arbitrary vector X a and imply the one-loop scale invariance of the GS sigma model. In the special case when X a is the gradient of a scalar ϕ (dilaton) one recovers the standard type I equations equivalent to the 2d Weyl invariance conditions of the superstring sigma model. In the type II case we find a generalized version of the 10d supergravity equations the bosonic part of which was introduced in arXiv:1511.05795. These equations depend on two vectors X a and K a subject to 1st order differential relations (with the equations in the NS-NS sector depending only on the combination X a = X a + K a ). In the special case of K a = 0 one finds that X a = ∂ a ϕ and thus obtains the standard type II supergravity equations. New generalized solutions are found if K a is chosen to be a Killing vector (and thus they exist only if the metric admits an isometry). Non-trivial solutions of the generalized equations describe K-isometric backgrounds that can be mapped by T-duality to type II supergravity solutions with dilaton containing a linear isometry-breaking term. Examples of such backgrounds appeared recently in the context of integrable η-deformations of AdS n × S n sigma models. The classical kappa-symmetry thus does not, in general, imply the 2d Weyl invariance conditions for the GS sigma model (equivalent to type II supergravity equations) but only weaker scale invariance type conditions.
Beccaria M, Tseytlin AA, 2016, Iterating free-field AdS/CFT: higher spin partition function relations, Journal of Physics A-Mathematical and Theoretical, Vol: 49, ISSN: 1751-8121
We find a simple relation between a free higher spin partition function on the thermal quotient of ${\mathrm{AdS}}_{d+1}$ and the partition function of the associated d-dimensional conformal higher spin field defined on the thermal quotient of ${\mathrm{AdS}}_{d}$. Starting with a conformal higher spin field defined in ${\mathrm{AdS}}_{d}$, one may also associate to with another conformal field in $d-1$ dimensions, thus iterating AdS/CFT. We observe that in the case of $d=4$, this iteration leads to a trivial 3d higher spin conformal theory with parity-even non-local action: it describes a zero total number of dynamical degrees of freedom and the corresponding partition function is equal to 1.
Ponomarev D, Tseytlin AA, 2016, On quantum corrections in higher-spin theory in flat space, Journal of High Energy Physics, Vol: 2016, ISSN: 1126-6708
We consider an interacting theory of an infinite tower of massless higher-spin fields in flat space with cubic vertices and their coupling constants found previously by Metsaev. We compute the one-loop bubble diagram part of the self-energy of the spin 0 member of the tower by summing up all higher-spin loop contributions. We find that the result contains an exponentially UV divergent part and we discuss how it could be cancelled by a tadpole contribution depending on yet to be determined quartic interaction vertex. We also compute the tree-level four-scalar scattering amplitude due to all higher-spin exchanges and discuss its inconsistency with the BCFW constructibility condition. We comment on possible relation to similar computations in AdS background in connection with AdS/CFT.
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