## Publications

234 results found

Hanany A, Sperling M, 2022, Magnetic quivers and negatively charged branes, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

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- Citations: 1

Gledhill K, Hanany A, 2022, Poisson Brackets for some Coulomb Branches

We construct Poisson bracket relations between the operators which generatethe chiral ring of the Coulomb branch of certain $3d$ $\mathcal{N}=4$ quivergauge theories. In the case where the Coulomb branch is a free space, $ADE$Klein singularity, or the minimal $A_2$ nilpotent orbit, we explicitly computethe Poisson brackets between the generators using either inherited propertiesof the abstract Coulomb branch variety, or the expected charges of theseoperators under the global symmetry (known through use of the monopoleformula). We also conjecture Poisson brackets for Higgs branches that originatefrom $6d$ theories with tensionless strings or $5d$ theories with masslessinstantons for which the HWG is known, based on representation theoretic andoperator content constraints known from the study of their magnetic quiver.

Bourget A, Grimminger JF, Hanany A,
et al., 2022, The Hasse diagram of the moduli space of instantons, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

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- Citations: 2

Bourget A, Grimminger JF, Hanany A,
et al., 2022, Higgs branches of U/SU quivers via brane locking, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

Bourget A, Dancer A, Grimminger JF,
et al., 2022, Partial implosions and quivers, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

Bao J, Hanany A, He YH,
et al., 2022, Some Open Questions in Quiver Gauge Theory, *Proyecciones*, Vol: 41, Pages: 355-386, ISSN: 0716-0917

Quivers, gauge theories and singular geometries are of great interest in both mathematics and physics. In this note, we collect a few open questions which have arisen in various recent works at the intersection between gauge theories, representation theory, and algebraic geometry. The questions originate from the study of supersymmetric gauge theories in different dimensions with different supersymmetries. Although these constitute merely the tip of a vast iceberg, we hope this guide can give a hint of possible directions in future research.

Gledhill K, Hanany A, 2021, Coulomb branch global symmetry and quiver addition, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

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- Citations: 4

Bourget A, Grimminger JF, Hanany A,
et al., 2021, Folding orthosymplectic quivers, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

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- Citations: 6

Bourget A, Dancer A, Grimminger JF,
et al., 2021, Orthosymplectic implosions, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

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- Citations: 5

Bourget A, Grimminger JF, Hanany A, et al., 2021, Branes, Quivers, and the Affine Grassmannian

Brane systems provide a large class of gauge theories that arise in stringtheory. This paper demonstrates how such brane systems fit with a somewhatexotic geometric object, called the affine Grassmannian. This gives a strongmotivation to study physical aspects of the affine Grassmannian. Explicitquivers are presented throughout the paper, and a quiver addition algorithm togenerate the affine Grassmannian is introduced. An important outcome of thisstudy is a set of quivers for new elementary slices.

Bourget A, Giacomelli S, Grimminger JF,
et al., 2021, S-fold magnetic quivers, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

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- Citations: 20

Bourget A, Hanany A, Miketa D, 2021, Quiver origami: discrete gauging and folding, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

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- Citations: 9

Dancer A, Hanany A, Kirwan F, 2021, Symplectic duality and implosions, *ADVANCES IN THEORETICAL AND MATHEMATICAL PHYSICS*, Vol: 25, Pages: 1367-1387, ISSN: 1095-0761

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- Citations: 3

Bourget A, Grimminger JF, Hanany A,
et al., 2020, Magnetic lattices for orthosymplectic quivers, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

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- Citations: 19

Bourget A, Grimminger JF, Hanany A,
et al., 2020, Magnetic quivers for rank 1 theories, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

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- Citations: 25

Hanany A, Zajac A, 2020, Ungauging schemes and Coulomb branches of non-simply laced quiver theories, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

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- Citations: 7

Grimminger JF, Hanany A, 2020, Hasse diagrams for 3d N=4 quiver gauge theories - Inversion and the full moduli space, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

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- Citations: 23

Bourget A, Grimminger JF, Hanany A,
et al., 2020, Magnetic quivers from brane webs with O5 planes, *The Journal of High Energy Physics*, Vol: 2020, Pages: 1-82, ISSN: 1029-8479

Magnetic quivers have led to significant progress in the understanding of gauge theories with 8 supercharges at UV fixed points. For a given low-energy gauge theory realised via a Type II brane construction, there exist magnetic quivers for the Higgs branches at finite and infinite gauge coupling. Comparing these moduli spaces allows one to study the non-perturbative effects when transitioning to the fixed point. For 5d N = 1 SQCD, 5-brane webs have been an important tool for deriving magnetic quivers. In this work, the emphasis is placed on 5-brane webs with orientifold 5-planes which give rise to 5d theories with orthogonal or symplectic gauge groups. For this set-up, the magnetic quiver prescription is derived and contrasted against a unitary magnetic quiver description extracted from an O7− construction. Further validation is achieved by a derivation of the associated Hasse diagrams. An important class of families considered are the orthogonal exceptional En families (−∞ < n ≤ 8), realised as infinite coupling Higgs branches of Sp(k) gauge theories with fundamental matter. In particular, the moduli spaces are realised by a novel type of magnetic quivers, called unitary-orthosymplectic quivers.

Grimminger JF, Hanany A, 2020, 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.

Hanany A, Kalveks R, 2020, Quiver theories and Hilbert series of classical Slodowy intersections, *NUCLEAR PHYSICS B*, Vol: 952, ISSN: 0550-3213

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- Citations: 7

Cabrera S, Hanany A, Sperling M, 2020, Magnetic quivers, Higgs branches, and 6d N = (1,0) theories - orthogonal and symplectic gauge groups, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

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- Citations: 26

Bourget A, Cabrera S, Grimminger JF, et al., 2020, The Higgs mechanism - Hasse diagrams for symplectic singularities, Publisher: SPRINGER

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- Citations: 51

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

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- Citations: 20

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

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