# Amihay Hanany

Faculty of Natural SciencesDepartment of Physics

Professor of Theoretical Physics

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### Contact

+44 (0)20 7594 3634a.hanany

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### Location

611Huxley BuildingSouth Kensington Campus

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## Publications

Publication Type
Year
to

162 results found

Cabrera S, Hanany A, Zhong Z, Nilpotent orbits and the Coulomb branch of $T^σ(G)$ theories: special orthogonal vs orthogonal gauge group factors

Coulomb branches of a set of $3d\ \mathcal{N}=4$ supersymmetric gaugetheories are closures of nilpotent orbits of the algebra $\mathfrak{so}(n)$.From the point of view of string theory, these quantum field theories can beunderstood as effective gauge theories describing the low energy dynamics of abrane configuration with the presence of orientifold planes. The presence ofthe orientifold planes raises the question to whether the orthogonal factors ofa the gauge group are indeed orthogonal $O(N)$ or special orthogonal $SO(N)$.In order to investigate this problem, we compute the Hilbert series for theCoulomb branch of $T^\sigma(SO(n)^\vee)$ theories, utilizing the monopoleformula. The results for all nilpotent orbits from $\mathfrak {so} (3)$ to$\mathfrak{so}(10)$ which are special and normal are presented. A newrelationship between the choice of $SO/O(N)$ factors in the gauge group and theLusztig's Canonical Quotient of the corresponding nilpotent orbit is observed.We also provide a new way of projecting several magnetic lattices of different$SO(N)$ gauge group factors by the simultaneous action of a $\mathbb Z_2$group.

JOURNAL ARTICLE

Cheng G, Hanany A, Li Y, Zhao Yet al., Coulomb Branch for A-type Balanced Quivers in 3d $\mathcal{N}=4$ gauge theories

We study Coulomb branch moduli spaces of a class of three dimensional$\mathcal{N}=4$ gauge theories whose quiver satisfies the balance condition.The Coulomb branch is described by dressed monopole operators which can becounted using the Monopole formula. We mainly focus on A-type quivers in thispaper, using Hilbert Series to study their moduli spaces, and present theinteresting pattern which emerges. All of these balanced A-type quiver gaugetheories can be realized on brane intervals in Type IIB string theory, wheremirror symmetry acts by exchanging the five branes and induces an equivalencebetween Coulomb branch and Higgs branch of mirror pairs. For each theory, weexplicitly discuss the gauge invariant generators on the Higgs branch and therelations they satisfy. Finally, some analysis on $D_4$ balanced quivers alsopresents an interesting structure of their moduli spaces.

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Ferlito G, Hanany A, A tale of two cones: the Higgs Branch of Sp(n) theories with 2n flavours

The purpose of this short note is to highlight a particular phenomenon whichconcerns the Higgs branch of a certain family of 4d N = 2 theories with SO(2N)flavour symmetry. By studying the Higgs branch as an algebraic variety throughHilbert series techniques we find that it is not a single hyperkahler cone butrather the union of two cones with intersection a hyperkahler subvariety whichwe specify. This remarkable phenomenon is not only interesting per se but playsa crucial role in understanding the structure of all Higgs branches that aregenerated by mesons.

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Hanany A, Kalveks R, Quiver Theories and Formulae for Nilpotent Orbits of Exceptional Algebras

We treat the topic of the closures of the nilpotent orbits of the Liealgebras of Exceptional groups through their descriptions as moduli spaces, interms of Hilbert series and the highest weight generating functions for theirrepresentation content. We extend the set of known Coulomb branch quiver theoryconstructions for Exceptional group minimal nilpotent orbits, or reduced singleinstanton moduli spaces, to include all orbits of Characteristic Height 2,drawing on extended Dynkin diagrams and the unitary monopole formula. We alsopresent a representation theoretic formula, based on localisation methods, forthe normal nilpotent orbits of the Lie algebras of any Classical or Exceptionalgroup. We analyse lower dimensioned Exceptional group nilpotent orbits in termsof Hilbert series and the Highest Weight Generating functions for theirdecompositions into characters of irreducible representations and/or HallLittlewood polynomials. We investigate the relationships between the modulispaces describing different nilpotent orbits and propose candidates for theconstructions of some non-normal nilpotent orbits of Exceptional algebras.

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Hanany A, Pini A, HWG for Coulomb branch of $3d$ Sicilian theory mirrors

Certain star shaped quivers exhibit a pattern of symmetry enhancement on theCoulomb branch of $3d$ $\mathcal{N}=4$ supersymmetric gauge theories. Thispaper studies a subclass of theories where such global symmetry enhancementoccurs through a computation of the Highest Weight Generating Function (HWG)and of the corresponding Hilbert Series (HS), providing a further test of theCoulomb branch formula. This special subclass has a feature in which the HWGtakes a particularly simple form, as a simple rational function which is eithera product of simple poles (termed freely generated) or a simple PE (termedcomplete intersection). Out of all possible star shaped quivers, this is aparticularly simple subclass. The present study motivates a further study ofidentifying all star shaped quivers for which their HWG is of this simple form.

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

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

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

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

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

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Hanany A, Hwang C, Kim H, Park J, Seong R-Ket al., 2016, Hilbert series for theories with Aharony duals (vol 2015, 132, 2015), JOURNAL OF HIGH ENERGY PHYSICS, ISSN: 1029-8479

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Hanany A, Jejjala V, Ramgoolam S, Seong R-Ket al., 2016, Consistency and derangements in brane tilings, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 49, ISSN: 1751-8113

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Hanany A, Kalveks R, 2016, Quiver theories for moduli spaces of classical group nilpotent orbits, JOURNAL OF HIGH ENERGY PHYSICS, ISSN: 1029-8479

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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

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Hanany A, Sperling M, 2016, Coulomb branches for rank 2 gauge groups in 3d N=4 gauge theories, JOURNAL OF HIGH ENERGY PHYSICS, ISSN: 1029-8479

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Cremonesi S, Hanany A, Mekareeya N, Zaffaroni Aet 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

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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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Hanany A, Hwang C, Kim H, Park J, Seong R-Ket al., 2015, Hilbert series for theories with Aharony duals, JOURNAL OF HIGH ENERGY PHYSICS, ISSN: 1029-8479

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Hanany A, Kalveks R, 2015, Construction and deconstruction of single instanton Hilbert series, JOURNAL OF HIGH ENERGY PHYSICS, Pages: 1-83, ISSN: 1029-8479

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Hanany A, Maruyoshi K, 2015, Chiral theories of class S, JOURNAL OF HIGH ENERGY PHYSICS, Pages: 1-32, ISSN: 1029-8479

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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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Bianchi M, Cremonesi S, Hanany A, Morales JF, Pacifici DR, Seong R-Ket al., 2014, Mass-deformed brane tilings, JOURNAL OF HIGH ENERGY PHYSICS, ISSN: 1029-8479

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

JOURNAL ARTICLE

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

JOURNAL ARTICLE

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

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

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Dey A, Hanany A, Mekareeya N, Rodriguez-Gomez D, Seong R-Ket 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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Hanany A, Kalveks R, 2014, Highest weight generating functions for Hilbert series, JOURNAL OF HIGH ENERGY PHYSICS, ISSN: 1029-8479

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

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