## Publications

224 results found

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

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

Hanany A, Zajac A, 2020, Ungauging schemes and Coulomb branches of non-simply laced quiver theories, *Journal of High Energy Physics*, Vol: 2020

© 2020, The Author(s). Three dimensional Coulomb branches have a prominent role in the study of moduli spaces of supersymmetric gauge theories with 8 supercharges in 3, 4, 5, and 6 dimensions. Inspired by simply laced 3d N = 4 supersymmetric quiver gauge theories, we consider Coulomb branches constructed from non-simply laced quivers with edge multiplicity k and no flavor nodes. In a computation of the Coulomb branch as the space of dressed monopole operators, a center-of-mass U(1) symmetry needs to be ungauged. Typically, for a simply laced theory, all choices of the ungauged U(1) (i.e. all choices of ungauging schemes) are equivalent and the Coulomb branch is unique. In this note, we study various ungauging schemes and their effect on the resulting Coulomb branch variety. It is shown that, for a non-simply laced quiver, inequivalent ungauging schemes exist which correspond to inequivalent Coulomb branch varieties. Ungauging on any of the long nodes of a non-simply laced quiver yields the same Coulomb branch C. For choices of ungauging the U(1) on a short node of rank higher than 1, the GNO dual magnetic lattice deforms anisotropically such that it no longer corresponds to a Lie group, and therefore, the monopole formula yields a non-valid Coulomb branch. However, if the ungauging is performed on a short node of rank 1, the one-dimensional magnetic lattice is rescaled along its single direction i.e. isotropically and the corresponding Coulomb branch is an orbifold of the form C/ℤk. Ungauging schemes of 3d Coulomb branches provide a particularly interesting and intuitive description of a subset of actions on the nilpotent orbits studied by Kostant and Brylinski [1]. The ungauging scheme analysis is carried out for minimally unbalanced Cn, affine F4, affine G2, and twisted affine D4(3) quivers, respectively. The analysis is complemented with computations of the Highest Weight Generating functions.

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.

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

- Author Web Link
- Cite
- Citations: 2

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

- Author Web Link
- Cite
- Citations: 5

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

- Author Web Link
- Cite
- Citations: 10

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

- Author Web Link
- Cite
- Citations: 2

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

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, Sperling M, 2018, Discrete quotients of 3-dimensional N=4 Coulomb branches via the cycle index, *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

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

This data is extracted from the Web of Science and reproduced under a licence from Thomson Reuters. You may not copy or re-distribute this data in whole or in part without the written consent of the Science business of Thomson Reuters.