## Publications

214 results found

Bourget A, Cabrera S, Grimminger JF, et al., 2020, The Higgs mechanism — Hasse diagrams for symplectic singularities

© 2020, The Author(s). We explore the geometrical structure of Higgs branches of quantum field theories with 8 supercharges in 3, 4, 5 and 6 dimensions. They are symplectic singularities, and as such admit a decomposition (or foliation) into so-called symplectic leaves, which are related to each other by transverse slices. We identify this foliation with the pattern of partial Higgs mechanism of the theory and, using brane systems and recently introduced notions of magnetic quivers and quiver subtraction, we formalise the rules to obtain the Hasse diagram which encodes the structure of the foliation. While the unbroken gauge symmetry and the number of flat directions are obtainable by classical field theory analysis for Lagrangian theories, our approach allows us to characterise the geometry of the Higgs branch by a Hasse diagram with symplectic leaves and transverse slices, thus refining the analysis and extending it to non-Lagrangian theories. Most of the Hasse diagrams we obtain extend beyond the cases of nilpotent orbit closures known in the mathematics literature. The geometric analysis developed in this paper is applied to Higgs branches of several Lagrangian gauge theories, Argyres-Douglas theories, five dimensional SQCD theories at the conformal fixed point, and six dimensional SCFTs.

Bourget A, Cabrera S, Grimminger JF, et al., 2019, Brane webs and magnetic quivers for SQCD, Publisher: arXiv

It is widely considered that the classical Higgs branch of 4d $\mathcal{N}=2$SQCD is a well understood object. However there is no satisfactoryunderstanding of its structure. There are two complications: (1) the Higgsbranch chiral ring contains nilpotent elements, as can easily be checked in thecase of $\mathrm{SU}(N)$ with 1 flavour. (2) the Higgs branch as a geometricspace can in general be decomposed into two cones with nontrivial intersection,the baryonic and mesonic branches. To study the second point in detail we usethe recently developed tool of magnetic quivers for five-brane webs, using thefact that the classical Higgs branch for theories with 8 supercharges does notchange through dimensional reduction. We compare this approach with thecomputation of the hyper-K\"ahler quotient using Hilbert series techniques,finding perfect agreement if nilpotent operators are eliminated by thecomputation of a so called radical. We study the nature of the nilpotentoperators and give conjectures for the Hilbert series of the full Higgs branch,giving new insights into the vacuum structure of 4d $\mathcal{N}=2$ SQCD. Inaddition we demonstrate the power of the magnetic quiver technique, as itallows us to identify the decomposition into cones, and provides us with theglobal symmetries of the theory, as a simple alternative to the techniques thatwere used to date.

Cabrera S, Hanany A, Sperling M, 2019, Magnetic quivers, Higgs branches and 6d N = (1, 0) theories (vol 2019, 071, 2019), *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

Cabrera S, Hanany A, Sperling M, 2019, Magnetic quivers, Higgs branches and 6d N = (1,0) theories, *Journal of High Energy Physics*, Vol: 71, Pages: 1-53, ISSN: 1029-8479

The physics of M5 branes placed near an M9 plane on an A-type ALE singularity exhibits a variety of phenomena that introduce additional massless degrees of freedom. There are tensionless strings whenever two M5 branes coincide or whenever an M5 brane approaches the M9 plane. These systems do not admit a low-energy Lagrangian description so new techniques are desirable to shed light on the physics of these phenomena. The 6-dimensional =(1,0) world-volume theory on the M5 branes is composed of massless vector, tensor, and hyper multiplets, and has two branches of the vacuum moduli space where either the scalar fields in the tensor or hyper multiplets receive vacuum expectation values. Focusing on the Higgs branch of the low-energy theory, previous works suggest the conjecture that a new Higgs branch arises whenever a BPS-string becomes tensionless. Consequently, a single theory admits a multitude of Higgs branches depending on the types of tensionless strings in the spectrum. The two main phenomena discrete gauging and small E8instanton transition can be treated in a concise and effective manner by means of Coulomb branches of 3-dimensional =4 gauge theories. In this paper, a formalism is introduced that allows to derive a novel object from a brane configuration, called the magnetic quiver. The main features are as follows: (i) the 3d Coulomb branch of the magnetic quiver yields the Higgs branch of the 6d system, (ii) all discrete gauging and E8 instanton transitions have an explicit brane realisation, and (iii) exceptional symmetries arise directly from brane configurations. The formalism facilitates the description of Higgs branches at finite and infinite gauge coupling as spaces of dressed monopole operators.

Hanany A, Okazaki T, 2019, (0,4) brane box models, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

Cabrera S, Hanany A, Zajac A, 2019, Minimally unbalanced quivers, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

Hanany A, Miketa D, 2019, Nilpotent orbit Coulomb branches of types AD, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

Cabrera S, Hanany A, Kalveks R, 2019, Quiver theories and formulae for Slodowy slices of classical algebras, *NUCLEAR PHYSICS B*, Vol: 939, Pages: 308-357, ISSN: 0550-3213

Cabrera S, Hanany A, Yagi F, 2019, Tropical geometry and five dimensional Higgs branches at infinite coupling, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

Bachas C, Bianchi M, Hanany A, 2018, N = 2 moduli of AdS(4) vacua: a fine-print study (vol 08, 100, 2018), *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

Cabrera S, Hanany A, 2018, Quiver subtractions, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

Hanany A, Sperling M, 2018, Resolutions of nilpotent orbit closures via Coulomb branches of 3-dimensional = N=4 theories, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

Hanany A, Zajac A, 2018, Discrete gauging in Coulomb branches of three dimensional N=4 supersymmetric gauge theories, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

Hanany A, Sperling M, 2018, Discrete quotients of 3-dimensional N=4 Coulomb branches via the cycle index, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

Bachas C, Bianchi M, Hanany A, 2018, N=2 moduli of AdS(4) vacua: a fine-print study, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

Hanany A, Zafrir G, 2018, Discrete gauging in six dimensions, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

Hanany A, Mekareeya N, 2018, The small E-8 instanton and the Kraft Procesi transition, *Journal of High Energy Physics*, Vol: 2018, ISSN: 1029-8479

One of the simplest (1, 0) supersymmetric theories in six dimensions lives on the world volume of one M5 brane at a D type singularity ℂ2/Dk. The low energy theory is given by an SQCD theory with Sp(k − 4) gauge group, a precise number of 2k flavors which is anomaly free, and a scale which is set by the inverse gauge coupling. The Higgs branch at finite coupling ℋ is a closure of a nilpotent orbit of D2k and develops many more flat directions as the inverse gauge coupling is set to zero (violating a standard lore that wrongly claims the Higgs branch remains classical). The quaternionic dimension grows by 29 for any k and the Higgs branch stops being a closure of a nilpotent orbit for k > 4, with an exception of k = 4 where it becomes min 8¯, the closure of the minimal nilpotent orbit of E8, thus having a rare phenomenon of flavor symmetry enhancement in six dimensions. Geometrically, the natural inclusion of ℋ ⊂ℋ∞ fits into the Brieskorn Slodowy theory of transverse slices, and the transverse slice is computed to be min 8¯ for any k > 3. This is identified with the well known small E8 instanton transition where 1 tensor multiplet is traded with 29 hypermultiplets, thus giving a physical interpretation to the geometric theory. By the analogy with the classical case, we call this the Kraft Procesi transition.

Ferlito G, Hanany A, Mekareeya N,
et al., 2018, 3d Coulomb branch and 5d Higgs branch at infinite coupling, *Journal of High Energy Physics*, Vol: 2018, ISSN: 1029-8479

The Higgs branch of minimally supersymmetric five dimensional SQCD theories increases in a significant way at the UV fixed point when the inverse gauge coupling is tuned to zero. It has been a long standing problem to figure out how, and to find an exact description of this Higgs branch. This paper solves this problem in an elegant way by proposing that the Coulomb branches of three dimensional =4 supersymmetric quiver gauge theories, named “Exceptional Sequences”, provide the solution to the problem. Thus, once again, 3d =4 Coulomb branches prove to be useful tools in solving problems in higher dimensions. Gauge invariant operators on the 5d side consist of classical objects such as mesons, baryons and gaugino bilinears, and non perturbative objects such as instanton operators with or without baryon number. On the 3d side we have classical objects such as Casimir invariants and non perturbative objects such as monopole operators, bare or dressed. The duality map works in a very interesting way.

Cabrera S, Hanany A, 2018, Branes and the Kraft-Procesi transition: classical case, *JOURNAL OF HIGH ENERGY PHYSICS*, Vol: 2018, ISSN: 1029-8479

Moduli spaces of a large set of 3d N=4 effective gauge theories are known to be closures of nilpotent orbits. This set of theories has recently acquired a special status, due to Namikawa’s theorem. As a consequence of this theorem, closures of nilpotent orbits are the simplest non-trivial moduli spaces that can be found in three dimensional theories with eight supercharges. In the early 80’s mathematicians Hanspeter Kraft and Claudio Procesi characterized an inclusion relation between nilpotent orbit closures of the same classical Lie algebra. We recently [1] showed a physical realization of their work in terms of the motion of D3-branes on the Type IIB superstring embedding of the effective gauge theories. This analysis is restricted to A-type Lie algebras. The present note expands our previous discussion to the remaining classical cases: orthogonal and symplectic algebras. In order to do so we introduce O3-planes in the superstring description. We also find a brane realization for the mathematical map between two partitions of the same integer number known as collapse. Another result is that basic Kraft-Procesi transitions turn out to be described by the moduli space of orthosymplectic quivers with varying boundary conditions.

Hanany A, Kalveks R, 2017, Quiver theories and formulae for nilpotent orbits of Exceptional algebras, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

Cabrera S, Hanany A, Zhong Z, 2017, Nilpotent orbits and the Coulomb branch of T-sigma(G) theories: special orthogonal vs orthogonal gauge group factors, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

Dey A, Hanany A, Koroteev P,
et al., 2017, On three-dimensional quiver gauge theories of type B, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

Bah I, Hanany A, Maruyoshi K,
et al., 2017, 4d N=1 from 6d N = (1,0) on a torus with fluxes, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

Cremonesi S, Ferlito G, Hanany A,
et al., 2017, Instanton operators and the Higgs branch at infinite coupling, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

Hanany A, Sperling M, 2017, Algebraic properties of the monopole formula, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

Cabrera S, Hanany A, 2016, Branes and the Kraft-Procesi transition, *JOURNAL OF HIGH ENERGY PHYSICS*, Vol: 2016, ISSN: 1029-8479

The Coulomb and Higgs branches of certain 3dN=4N=4 gauge theories can be understood as closures of nilpotent orbits. Recently, a new theorem by Namikawa suggests that this is the simplest possible case, thus giving this class a special role. In this note we use branes to reproduce the mathematical work by Kraft and Procesi. It studies the classification of all nilpotent orbits for classical groups and it characterizes an inclusion relation via minimal singularities. We show how these minimal singularities arise naturally in the Type IIB superstring embedding of the 3d A-type theories. The Higgs mechanism can be used to remove the minimal singularity, corresponding to a transition in the brane configuration that induces a new effective 3d theory. This reproduces the Kraft-Procesi results, endowing the family of gauge theories with a new underlying structure. We provide an efficient procedure for computing such brane transitions.

Hanany A, Ramgoolam S, Rodriguez-Gomez D, 2016, Highest weight generating functions for hyperKahler T*(G/H)spaces, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

Hanany A, Jejjala V, Ramgoolam S,
et al., 2016, Consistency and derangements in brane tilings, *Journal of Physics A - Mathematical and Theoretical*, Vol: 49, ISSN: 1751-8113

Brane tilings describe Lagrangians (vector multiplets, chiral multiplets, and the superpotential) of four-dimensional ${ \mathcal N }=1$ supersymmetric gauge theories. These theories, written in terms of a bipartite graph on a torus, correspond to worldvolume theories on N D3-branes probing a toric Calabi–Yau threefold singularity. A pair of permutations compactly encapsulates the data necessary to specify a brane tiling. We show that geometric consistency for brane tilings, which ensures that the corresponding quantum field theories are well behaved, imposes constraints on the pair of permutations, restricting certain products constructed from the pair to have no one-cycles. Permutations without one-cycles are known as derangements. We illustrate this formulation of consistency with known brane tilings. Counting formulas for consistent brane tilings with an arbitrary number of chiral bifundamental fields are written down in terms of delta functions over symmetric groups.

Hanany A, Sperling M, 2016, Coulomb branches for rank 2 gauge groups in 3d N=4 gauge theories, *Journal of High Energy Physics*, Vol: 2016, ISSN: 1126-6708

The Coulomb branch of 3-dimensional N = 4 gauge theories is the space ofbare and dressed BPS monopole operators. We utilise the conformal dimension to define afan which, upon intersection with the weight lattice of a GNO-dual group, gives rise to acollection of semi-groups. It turns out that the unique Hilbert bases of these semi-groupsare a sufficient, finite set of monopole operators which generate the entire chiral ring.Moreover, the knowledge of the properties of the minimal generators is enough to computethe Hilbert series explicitly. The techniques of this paper allow an efficient evaluation ofthe Hilbert series for general rank gauge groups. As an application, we provide variousexamples for all rank two gauge groups to demonstrate the novel interpretation.

Hanany A, Kalveks R, 2016, Quiver theories for moduli spaces of classical group nilpotent orbits, *Journal of High Energy Physics*, Vol: 2016, ISSN: 1126-6708

We approach the topic of Classical group nilpotent orbits from the perspective of the moduli spaces of quivers, described in terms of Hilbert series and generating functions. We review the established Higgs and Coulomb branch quiver theory constructions for A series nilpotent orbits. We present systematic constructions for BCD series nilpotent orbits on the Higgs branches of quiver theories defined by canonical partitions; this paper collects earlier work into a systematic framework, filling in gaps and providing a complete treatment. We find new Coulomb branch constructions for above minimal nilpotent orbits, including some based upon twisted affine Dynkin diagrams. We also discuss aspects of 3d mirror symmetry between these Higgs and Coulomb branch constructions and explore dualities and other relationships, such as HyperKähler quotients, between quivers. We analyse all Classical group nilpotent orbit moduli spaces up to rank 4 by giving their unrefined Hilbert series and the Highest Weight Generating functions for their decompositions into characters of irreducible representations and/or Hall Littlewood polynomials.

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