## Publications

224 results found

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

Hanany A, Maruyoshi K, 2015, Chiral theories of class S, *Journal of High Energy Physics*, Vol: 2015, ISSN: 1126-6708

We study a class of four-dimensional N=1N=1 superconformal field theories obtained from the six-dimensional (1, 0) theory, on M5-branes on C2/ZkC2/Zk orbifold singularity, compactified on a Riemann surface. This produces various quiver gauge theories whose matter contents are chiral. We classify the building blocks associated to pairs-of-pants, and study the gauging of them as the gluing of punctures. The Riemann surface picture makes the duality invariance of the resulting quiver theories manifest: the theories associated to the same Riemann surface flow to the same nontrivial infrared fixed point. We explicitly check this from the ’t Hooft anomalies of the global symmetries and central charges.

Hanany A, Hwang C, Kim H,
et al., 2015, Hilbert series for theories with Aharony duals, *Journal of High Energy Physics*, Vol: 2015, ISSN: 1126-6708

The algebraic structure of moduli spaces of 3d N=2N=2 supersymmetric gauge theories is studied by computing the Hilbert series which is a generating function that counts gauge invariant operators in the chiral ring. These U(Nc) theories with Nf flavors have Aharony duals and their moduli spaces receive contributions from both mesonic and monopole operators. In order to compute the Hilbert series, recently developed techniques for Coulomb branch Hilbert series in 3d N=4N=4 are extended to 3d N=2N=2 . The Hilbert series computation leads to a general expression of the algebraic variety which represents the moduli space of the U(Nc) theory with Nf flavors and its Aharony dual theory. A detailed analysis of the moduli space is given, including an analysis of the various components of the moduli space.

Del Zotto M, Hanany A, 2015, Complete graphs, Hilbert series, and the Higgs branch of the 4d N=2 (A(n), A(m)) SCFTs, *NUCLEAR PHYSICS B*, Vol: 894, Pages: 439-455, ISSN: 0550-3213

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- Citations: 22

Hanany A, Seong R-K, 2015, Hilbert series and moduli spaces of k U(N) vortices, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

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- Citations: 7

Cremonesi S, Hanany A, Mekareeya N,
et al., 2015, T-rho(sigma) (G) theories and their Hilbert series, *Journal of High Energy Physics*, Vol: 2015, ISSN: 1126-6708

We give an explicit formula for the Higgs and Coulomb branch Hilbert seriesfor the class of 3d N = 4 superconformal gauge theories Tσρ(G) corresponding to a set ofD3 branes ending on NS5 and D5-branes, with or without O3 planes. Here G is a classicalgroup, σ is a partition of G and ρ a partition of the dual group G∨. In deriving such aformula we make use of the recently discovered formula for the Hilbert series of the quantumCoulomb branch of N = 4 superconformal theories. The result can be expressed in termsof a generalization of a class of symmetric functions, the Hall-Littlewood polynomials,and can be interpreted in mathematical language in terms of localization. We mainlyconsider the case G = SU(N) but some interesting results are also given for orthogonaland symplectic groups

Cremonesi S, Ferlito G, Hanany A,
et al., 2014, Coulomb branch and the moduli space of instantons, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

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- Citations: 40

Hanany A, Kalveks R, 2014, Highest weight generating functions for Hilbert series, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

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- Citations: 27

Bianchi M, Cremonesi S, Hanany A,
et al., 2014, Mass-deformed brane tilings, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

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- Citations: 6

Cremonesi S, Hanany A, Mekareeya N,
et al., 2014, Coulomb branch Hilbert series and Hall-Littlewood polynomials, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

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- Citations: 38

Cremonesi S, Hanany A, Mekareeya N,
et al., 2014, Coulomb branch Hilbert series and three dimensional Sicilian theories, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

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- Citations: 27

Dey A, Hanany A, Koroteev P,
et al., 2014, Mirror symmetry in three dimensions via gauged linear quivers, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

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- Citations: 9

Dey A, Hanany A, Mekareeya N,
et al., 2014, Hilbert series for moduli spaces of instantons on C-2/Z(n), *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

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- Citations: 19

Cremonesi S, Hanany A, Zaffaroni A, 2014, Monopole operators and Hilbert series of Coulomb branches of 3d N=4 gauge theories, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

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- Citations: 84

Hanany A, He Y-H, Sun C,
et al., 2013, Superconformal block quivers, duality trees and Diophantine equations, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

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- Citations: 4

Cremonesi S, Hanany A, Seong R-K, 2013, Double handled brane tilings, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

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- Citations: 10

Hanany A, Mekareeya N, Razamat SS, 2013, Hilbert series for moduli spaces of two instantons, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

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- Citations: 26

Hanany A, Seong R-K, 2012, Brane tilings and specular duality, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

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- Citations: 19

Hanany A, Seong R-K, 2012, Brane tilings and reflexive polygons, *FORTSCHRITTE DER PHYSIK-PROGRESS OF PHYSICS*, Vol: 60, Pages: 695-803, ISSN: 0015-8208

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- Citations: 29

Hanany A, He Y-H, Jejjala V,
et al., 2012, INVARIANTS OF TORIC SEIBERG DUALITY, *INTERNATIONAL JOURNAL OF MODERN PHYSICS A*, Vol: 27, ISSN: 0217-751X

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- Citations: 7

He Y-H, Candelas P, Hanany A,
et al., 2012, Computational Algebraic Geometry in String and Gauge Theory, *ADVANCES IN HIGH ENERGY PHYSICS*, Vol: 2012, ISSN: 1687-7357

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- Citations: 12

Hanany A, Mekareeya N, 2012, Complete intersection moduli spaces in N=4 gauge theories in three dimensions, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

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- Citations: 19

Davey J, Hanany A, Mekareeya N,
et al., 2011, M2-branes and Fano 3-folds, *JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL*, Vol: 44, ISSN: 1751-8113

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- Citations: 9

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