Imperial College London

Amihay Hanany

Faculty of Natural SciencesDepartment of Physics

Professor of Theoretical Physics



+44 (0)20 7594 3634a.hanany




611Huxley BuildingSouth Kensington Campus





Publication Type

224 results found

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.

Journal article

Bourget A, Giacomelli S, Grimminger JF, Hanany A, Sperling M, Zhong Zet al., S-fold magnetic quivers

Magnetic quivers and Hasse diagrams for Higgs branches of rank $r$ 4d$\mathcal{N}=2$ SCFTs arising from $\mathbb{Z}_{\ell}$ $\mathcal{S}$-foldconstructions are discussed. The magnetic quivers are derived using threedifferent methods: 1) Using clues like dimension, global symmetry, and thefolding parameter $\ell$ to guess the magnetic quiver. 2) From 6d$\mathcal{N}=(1,0)$ SCFTs as UV completions of 5d marginal theories, andspecific FI deformations on their magnetic quiver, which is further folded by$\mathbb{Z}_{\ell}$. 3) From T-duality of Type IIA brane systems of 6d$\mathcal{N}=(1,0)$ SCFTs and explicit mass deformation of the resulting braneweb followed by $\mathbb{Z}_{\ell}$ folding. A choice of the ungauging scheme,either on a long node or on a short node, yields two different moduli spacesrelated by an orbifold action, thus suggesting a larger set of SCFTs in fourdimensions than previously expected.

Journal article

Grimminger JF, Hanany A, Hasse Diagrams for $\mathbf{3d}$ $\mathbf{\mathcal{N}=4}$ Quiver Gauge Theories -- Inversion and the full Moduli Space

We study Hasse diagrams of moduli spaces of $\mathrm{3d}$ $\mathcal{N}=4$quiver gauge theories. The goal of this work is twofold: 1) We introduce thenotion of inverting a Hasse diagram and conjecture that the Coulomb branch andHiggs branch Hasse diagrams of certain theories are related through thisoperation. 2) We introduce a Hasse diagram to map out the entire moduli spaceof the theory, including the Coulomb, Higgs and mixed branches. For theorieswhose Higgs and Coulomb branch Hasse diagrams are related by inversion it isstraight forward to generate the Hasse diagram of the entire moduli space. Weapply inversion of the Higgs branch Hasse diagram in order to obtain theCoulomb branch Hasse diagram for bad theories and obtain results consistentwith the literature. For theories whose Higgs and Coulomb branch Hasse diagramsare not related by inversion it is nevertheless possible to produce the Hassediagram of the full moduli space using different methods. We give examples forHasse diagrams of the entire moduli space of theories with \emph{enhanced}Coulomb branches.

Journal article

Dancer A, Hanany A, Kirwan F, Symplectic duality and implosions

We discuss symplectic and hyperk\"ahler implosion and present candidates forthe symplectic duals of the universal hyperk\"ahler implosion for variousgroups.

Journal article

Bourget A, Hanany A, Miketa D, Quiver origami: discrete gauging and folding

We study two types of discrete operations on Coulomb branches of $3d$$\mathcal{N}=4$ quiver gauge theories using both abelianisation and themonopole formula. We generalise previous work on discrete quotients of Coulombbranches and introduce novel wreathed quiver theories. We further study quiverfolding which produces Coulomb branches of non-simply laced quivers.

Journal article

Bourget A, Grimminger JF, Hanany A, Kalveks R, Sperling M, Zhong Zet al., Magnetic Lattices for Orthosymplectic Quivers

For any gauge theory, there may be a subgroup of the gauge group which actstrivially on the matter content. While many physical observables are notsensitive to this fact, the identification of the precise gauge group becomescrucial when the magnetic spectrum of the theory is considered. This questionis addressed in the context of Coulomb branches for $3$d $\mathcal{N}=4$ quivergauge theories, which are moduli spaces of dressed monopole operators. Sincemonopole operators are characterized by their magnetic charge, theidentification of the gauge group is imperative for the determination of themagnetic lattice. It is well-known that the gauge group of unframed unitaryquivers is the product of all unitary nodes in the quiver modded out by thediagonal $\mathrm{U}(1)$ acting trivially on the matter representation. Thisreasoning generalises to the notion that a choice of gauge group associated toa quiver is given by the product of the individual nodes quotiented by anysubgroup that acts trivially on the matter content. For unframed (unitary-)orthosymplectic quivers composed of $\mathrm{SO}(\textrm{even})$,$\mathrm{USp}$, and possibly $\mathrm{U}$ gauge nodes, the maximal subgroupacting trivially is a diagonal $\mathbb{Z}_2$. For unframed unitary quiverswith a single $\mathrm{SU}(N)$ node it is $\mathbb{Z}_N$. We use this notion tocompute the Coulomb branch Hilbert series of many unitary-orthosymplecticquivers. Examples include nilpotent orbit closures of the exceptional E-typealgebras and magnetic quivers that arise from brane physics. This includesHiggs branches of theories with 8 supercharges in dimensions $4$, $5$, and $6$.A crucial ingredient in the calculation of exact refined Hilbert series is thealternative construction of unframed magnetic quivers from resolved Slodowyslices, whose Hilbert series can be derived from Hall-Littlewood polynomials.

Journal article

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.

Journal article

Hanany A, Kennaway KD, Dimer models and toric diagrams

We propose a duality between quiver gauge theories and the combinatorics ofdimer models. The connection is via toric diagrams together with multiplicitiesassociated to points in the diagram (which count multiplicities of fields inthe linear sigma model construction of the toric space). These multiplicitiesmay be computed from both sides and are found to agree in all known examples.The dimer models provide new insights into the quiver gauge theories: forexample they provide a closed formula for the multiplicities of arbitraryorbifolds of a toric space, and allow a new algorithmic method for exploringthe phase structure of the quiver gauge theory.

Journal article

Hanany A, On the Quantum Moduli Space of N=2 Supersymmetric Gauge Theories, Nucl.Phys. B, Vol: 466, Pages: 85-100

Families of hyper-elliptic curves which describe the quantum moduli spaces ofvacua of $N=2$ supersymmetric $SO(N_c)$ gauge theories coupled to $N_f$ flavorsof quarks in the vector representation are constructed. The quantum modulispaces for $2N_f < N_c-1$ are determined completely by imposing $R$-symmetry,instanton corrections and the proper classical singularity structure. Thesecurves are verified by residue calculations. The quantum moduli spaces for$2N_f\geq N_c-1$ theories are parameterized and their general structure isworked out using residue calculations. The exact metrics on the quantum modulispaces as well as the exact spectrum of stable massive states are derived. Theresults presented here together with recent results of Martinec and Warnerprovide a natural conjecture for the form of the curves for the other gaugegroups.

Journal article

Hanany A, He Y-H, M2-Branes and Quiver Chern-Simons: A Taxonomic Study

We initiate a systematic investigation of the space of 2+1 dimensional quivergauge theories, emphasising a succinct "forward algorithm". Few "orderparametres" are introduced such as the number of terms in the superpotentialand the number of gauge groups. Starting with two terms in the superpotential,we find a generating function, with interesting geometric interpretation, whichcounts the number of inequivalent theories for a given number of gauge groupsand fields. We demonstratively list these theories for some low numbersthereof. Furthermore, we show how these theories arise from M2-branes probingtoric Calabi-Yau 4-folds by explicitly obtaining the toric data of the vacuummoduli space. By observing equivalences of the vacua between markedly differenttheories, we see a new emergence of "toric duality".

Journal article

Falkovich G, Hanany A, Spectra of Conformal Turbulence

A set of different conformal solutions corresponding to a constant flux ofsquared vorticity is considered. Requiring constant fluxes of all inviscidvorticity invariants (higher powers of the vorticity), we come to theconclusion that the general turbulence spectrum should be given by Kraichnan'sexpression $E(k)\propto k\sp{-3}$. This spectrum, in particular, can beobtained as a limit of some subsequences of the conformal solutions.

Journal article

Frishman Y, Hanany A, Karliner M, On the Stability of Quark Solitons in QCD

We critically re-examine our earlier derivation of the effective low energyaction for QCD in 4 dimensions with chiral fields transforming non-triviallyunder both color and flavor, using the method of anomaly integration. We findseveral changes with respect to our previous results, leading to much morecompact expressions, and making it easier to compare with results of otherapproaches to the same problem. With the amended effective action, we find thatthere are no stable soliton solutions. In the context of the quark solitonprogram, we interpret this as an indication that the full low-energy effectiveaction must include additional terms, reflecting possible modifications atshort distances and/or the non-trivial structure of the gauge fields in thevacuum, such as $ <F_{\mu\nu}^2> \neq 0$. Such terms are absent in theformalism based on anomaly integration.

Journal article

Davey J, Hanany A, Seong R-K, Counting Orbifolds, JHEP

We present several methods of counting the orbifolds C^D/Gamma. A correspondence between counting orbifold actions on C^D, brane tilings, and toric diagrams in D-1 dimensions is drawn. Barycentric coordinates and scaling mechanisms are introduced to characterize lattice simplices as toric diagrams. We count orbifolds of C^3, C^4, C^5, C^6 and C^7. Some remarks are made on closed form formulas for the partition function that counts distinct orbifold actions.

Journal article

Franco S, Hanany A, He Y-H, Kazakopoulos Pet al., Duality Walls, Duality Trees and Fractional Branes

We compute the NSVZ beta functions for N = 1 four-dimensional quiver theoriesarising from D-brane probes on singularities, complete with anomalousdimensions, for a large set of phases in the corresponding duality tree. Whilethese beta functions are zero for D-brane probes, they are non-zero in thepresence of fractional branes. As a result there is a non-trivial RG behavior.We apply this running of gauge couplings to some toric singularities such asthe cones over Hirzebruch and del Pezzo surfaces. We observe the emergence instring theory, of ``Duality Walls,'' a finite energy scale at which the numberof degrees of freedom becomes infinite, and beyond which Seiberg duality doesnot proceed. We also identify certain quiver symmetries as T-duality-likeactions in the dual holographic theory.

Journal article

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