## Publications

212 results found

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*, ISSN: 1029-8479

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.

Hanany A, Hwang C, Kim H,
et al., 2016, Addendum to: Hilbert series for theories with Aharony duals, *Journal of High Energy Physics*, Vol: 2016, ISSN: 1126-6708

Hanany A, Kalveks R, 2015, Construction and deconstruction of single instanton Hilbert series, *Journal of High Energy Physics*, Vol: 2015, Pages: 1-83, ISSN: 1126-6708

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