arXiv subjects

Amihay Hanany

Publications and source records attributed to Amihay Hanany.

At least 19 recordsLinked to original sources

arXiv2026

Spin(N) Magnetic Quivers

This work introduces new magnetic quivers for $5\mathrm{d}$ $\mathcal N=1$ Spin(N) gauge theories with hypermultiplets in spinor representations at both finite and infinite coupling. Among them are new 3d $\mathcal{N}=4$ theories whose Coulomb and Higgs branches are isolated symplectic singularities, or a product of such spaces. These theories further expand the set of orthosymplectic quiver gauge theories whose Coulomb branch is a single isolated singularity, termed `minimal quivers'. Wreathings and foldings thereof realise quivers for non-simply laced nilpotent orbit closures.

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arXiv2026

New symplectic singularities from $SU(2)$ gauge theories

Families of $\mathrm{Sp}(1)\simeq\mathrm{SU}(2)$ gauge theories with eight supercharges are found to have a Higgs branch which is an isolated symplectic singularity. These are, in some sense, the most ``minimal'' gauge theories as they only Higgs to a trivial theory. The matter content is $N$ fundamental half-hypermultiplets and one half-hypermultiplet in the $\mathrm{Sym}^k$ representation where $k=1,3,5,7$. The cases of $k=1,3$ reproduce the known Kraft--Procesi construction for minimal nilpotent orbit closures of $\mathrm{SO}(N+1)$ and the $g\mathrm{SO}(N)$ singularities of \cite{Bourget:2025wsp}, respectively. The cases $k=5,7$ are new isolated symplectic singularities which are termed $h\mathrm{SO}(N)$ and $i\mathrm{SO}(N)$, respectively. The classification of these isolated symplectic singularities is argued for through the Higgs mechanism, with Hilbert series and highest weight generating (HWG) functions computed for some cases. Each of the $g\mathrm{SO}(N)$, $h\mathrm{SO}(N)$, and $i\mathrm{SO}(N)$ families has a (quaternionic) one-dimensional member; these are the Klein $A_3$, $E_6$, and $E_8$ singularities, respectively. Our construction hence provides realisations of these Klein singularities as Higgs branches (hyper-K\"ahler quotients) of $\mathrm{Sp}(1)$ gauge theories, complementary to Kronheimer's construction \cite{Kronheimer:1989zs} using the $\widehat A_3$, $\widehat E_6$, and $\widehat E_8$ affine quivers. The Klein $E_7$ singularity is also realised as a Higgs branch (hyper-K\"ahler quotient) of an $\mathrm{Sp}(1)\times\mathrm{O}(1)$ gauge theory.

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arXiv2026

A Tale of Two Orbits: Non-Simply Laced Mirror

A three-dimensional $\mathcal{N}=4$ gauge theory is constructed whose Higgs branch realizes the affine closure of the cotangent bundle of the minimal nilpotent orbit of $\mathfrak{sl}_n$. This space is a symplectic singularity recently identified by Fu and Liu as a $\mathrm{U}(1)$ hyperk\"ahler quotient of the closure of the minimal nilpotent orbit of $\mathfrak{so}_{2n+2}$. The theory arises by gauging an $\mathrm{SO}(2)\cong\mathrm{U}(1)$ subgroup of the flavour symmetry of $\mathrm{SU}(2)$ SQCD with $n+1$ flavours. The Hilbert series is computed and the stratification is determined. A non-simply laced magnetic quiver is proposed whose Coulomb branch reproduces the same singularity. Evidence is thereby provided for a mirror pair involving a non-simply laced quiver, further tested through quiver subtraction and Hasse diagram inversion. A related $\mathbb{Z}_2$ quotient of the magnetic lattice is also analysed, and the exceptional behaviour in the case $n=2$, where $A_1 \cong C_1$, is explained. This construction provides a concrete example in which the Higgs-branch structure associated with a non-simply laced magnetic quiver can be inferred and validated through its mirror dual.

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arXiv2026

5d Higgs branch and instanton magnetization

Higgs branches of 5d $Sp(k)$ theories with $N_f$ flavours, whether at weak or strong coupling, are described by a pair of instantons transforming as pure spinors of $SO(2N_f)$. The Poisson structure is constrained by symmetry arguments and implies that these Higgs branches are algebraic integrable systems; the degeneration of the symplectic form occurs when the spinor annihilators overlap. We argue that the stratification of the Higgs branch at infinite coupling corresponds to the alignment of the instantons weights, leading to a non vanishing magnetization, and their acquisition of a mass.

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arXiv2026

Quiver Maps, Nilpotent Orbits and Special Pieces of Nilcones

This paper explores 3d $\mathcal{N}=4$ quiver gauge theories whose moduli spaces represent nilpotent orbits, S\l odowy slices or, more generally, S\l odowy intersections, which span the Special Pieces of nilcones of Classical or Exceptional algebras. We introduce a map between magnetic and electric quivers containing symmetric group actions, such as wreathings (or loops), bouquets, and/or non-simply laced foldings, which can be related to symmetric subgroups of Lusztig's canonical quotient groups for Special Pieces. The map on quivers induces a map on nilpotent orbits that partially resolves the obstruction to quiver dualities presented by the non-involutive nature of the Lusztig Spaltenstein and Barbasch Vogan maps. We use Coulomb and Higgs branch quiver methods complemented by localisation formulae. Some new quivers for intersections within Exceptional nilcones are presented.

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arXiv2026

Quotient Quiver Subtraction -- Classical Groups

Quotient quiver subtraction is a simple combinatorial prescription for gauging Coulomb branch isometry subgroups of 3d $\mathcal{N}=4$ quiver gauge theories. This paper uses Type IIB brane constructions with $\mathrm{O5}$ planes to extend the prescription to gauge $\mathrm{Sp}(n),\;\mathrm{SO}(n)$, and $\mathrm{Sp}(n)$ coupled to a half-hypermultiplet Coulomb branch isometry subgroups of quivers with unitary gauge groups. The gauging procedure is no longer solely a subtraction -- additional steps change the graph type. The method is applied to provide alternative constructions of the Higgs branch of certain SCFTs in higher dimensions.

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arXiv2026

Symmetry Mitosis and Hasse Diagram Diamonds: A Note on Brane Configurations with $\mathrm{ON}^{0}$ Planes

This letter considers 3d $\mathcal{N}=4$ (unitary-)orthosymplectic quiver gauge theories originating from Type IIA and Type IIB brane systems with $\mathrm{ON}^0$ planes. Such theories lie outside the scope of present combinatorial techniques for Coulomb branch symmetry and symplectic stratification. It turns out that the correct prescription involves `symmetry mitosis': a common subset of nodes in two linear balanced chains source \emph{two} factors of a Coulomb branch global symmetry instead of one; the correct Coulomb branch Hasse diagram is obtained by a `doubling' procedure on that computed by naive quiver subtraction. Input from 6d SQFTs and little string theories allows for the construction of various `mitotic' magnetic quivers. The full Higgs branch Hasse diagram of minimal $(E_6,E_6)$ conformal matter is given. Additionally, a new Type I$'$ brane system using eight full D8 branes, negatively charged D6 branes, and $\mathrm{ON}^0$ planes is found corresponding to a product of $\mathrm{Spin}(32)$ instantons on $\mathbb C^2$. The corresponding 6d theory uses $\mathrm{Sp}(-1)$ gauge nodes which have the interpretation of bi-spinor matter of $\mathrm{O}(a)$ and $\mathrm{O}(12-a)$ for $a=0,1,\cdots,12$.

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arXiv2025

Chiral ring along the RG flow in 5d $\mathcal{N}=1$

We compute the Higgs branch chiral ring of a simple class of 5d theories at strong coupling. A deformation by the instanton mass implies that the chiral ring at weak coupling is renormalized by a nilpotent operator, the gaugino bilinear. Consequently, F-term equations alone do not suffice to completely determine the moduli space of vacua and perturbative non-renormalization arguments are invalidated.

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arXiv2025

Higgs branch of 5d $\mathcal{N}=1$ symplectic gauge theories and dressed instanton operators

We expand in instanton charge sectors the representation content of the infinite coupling chiral ring of the Higgs branch of 5d $\mathcal{N}=1$ $Sp(k)$ theories with $N_f$ flavours. The entire chiral ring can be expressed as the product of bare instantons, one for each topological sector, times a common dressing factor depending on the mesons and the instanton-anti instanton bound state. The dressing factor, which is independent of the instanton number, encodes the chiral ring of the theory at finite coupling with one additional colour.

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arXiv2025

Orthosymplectic Quotient Quiver Subtraction II: Framed Quivers

The technique of $\textit{orthosymplectic quotient quiver subtraction}$ is introduced for framed orthosymplectic quivers. This involves subtracting an $\textit{orthosymplectic quotient quiver}$ from a framed orthosymplectic $3d\;\mathcal N=4$ quiver gauge theory which has the effect of gauging an $\mathrm{SO}(n)$ or $\mathrm{Sp}(n)$ subgroup of the IR Coulomb branch global symmetry with complete Higgsing. The orthosymplectic quotient quivers take the form of magnetic quivers for class $\mathcal S$ theories on cylinders with (twisted) maximal punctures of simply laced algebras, similar to the case of unitary quotient quiver subtraction. This gives a set of quotient quivers for all classical groups. Notably, quotient quiver subtraction for framed and unframed orthosymplectic quivers are different procedures.

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arXiv2025

3d Mirrors and Phase Diagrams of Abelian Gauge Theories

This paper presents new developments in the study of 3d mirror symmetry and the phase structure of Abelian gauge theories. Previous works identified 3d mirrors for a specific class of theories, termed ``simple" Abelian theories. This work extends this framework by proposing 3d mirrors for ``non-simple" Abelian theories with both discrete and continuous gauge group factors. The proposal is supported by evidence from an exact operator map between the Higgs/Coulomb branch of one theory and the Coulomb/Higgs branch of its 3d mirror. Further support is provided by explicit Hilbert series computations. An algorithm for computing the Hasse (phase) diagram of the Higgs branch of both simple and non-simple Abelian theories is introduced, uncovering a recently discovered family of isolated singularities among the elementary slices. A bottom-up algorithm for computing the Coulomb branch Hasse diagram of these theories is also introduced, and the two algorithms are tested against each other via 3d mirror symmetry.

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arXiv2025

$\mathrm{O}$/$\mathrm{SO}$ Gauge Groups, $BC$ Quivers and $O3$ Planes

D3-/D5-/NS5-brane systems with $O3$ orientifold planes realise 3d $\mathcal{N}=4$ gauge theories with orthogonal and symplectic gauge groups on the D3-brane worldvolume. Such setups have long contained an ambiguity regarding the global form of $D$-type gauge groups. This note offers a partial prescription for reading $\mathrm{O}(2k)$ and $\mathrm{SO}(2k)$ gauge nodes in orthosymplectic quivers using the presence of $\frac{1}{2}$D5-branes on the orientifolds bordering $\frac{1}{2}$NS5-brane intervals spanned by $O3^{-}$ planes. A set of identities are proposed relating the Coulomb branches of generic quivers under a Higgsing that relates $\mathrm{SO}(2k+1)$ and $\mathrm{O}(2k)$ gauge groups. A further prescription is conjectured regarding the action of $\frac{1}{2}$D5-branes on maximal $DC$-chains.

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arXiv2024

On brane systems with O${}^+$ planes -- 5d and 6d SCFTs

We study Higgs branches of field theories with 8 supercharges in 5 and 6 dimensions, focusing on theories realised on 5-brane webs in Type IIB with an O$7^+$ plane, or a D6-D8-NS5 brane system in Type IIA in the presence of an O$8^+$ plane. We find magnetic quivers for the Higgs branches of these theories. The main consequence of the presence of the orientifold is that it renders the magnetic quiver to be non-simply-laced. We propose a contribution of the O$7^+$ to the usual stable intersection number of 5-branes from tropical geometry, and show that it is consistent with Fayet-Iliopoulos deformations of magnetic quivers which represent mass deformations of 5d SQFTs. From the magnetic quivers, we compute phase diagrams and highest weight generating functions for the Higgs branches, enabling us to identify the global form of the flavour symmetry for several families of 5d SQFTs; among them Bhardwaj's rank-1 theory. For 6d theories realised on a $-4$ curve, we observe the appearance of an additional $D_4$ slice on top of the phase diagram as one goes to the tensionless limit.

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arXiv2024

Quiver Subtraction on the Higgs Branch

This paper classifies all Higgs branch Higgsing patterns for simply-laced unitary quiver gauge theories with eight supercharges (including multiple loops) and introduces a Higgs branch subtraction algorithm. All possible minimal transitions are given, identifying differences between slices that emerge on the Higgs and Coulomb branches. In particular, the algorithm is sensitive to global information including monodromies and Namikawa-Weyl groups. Guided by symplectic duality, the algorithm further determines the global symmetry on the Coulomb branch, and verifies the exclusion of $C$ type or $F_4$ global symmetry for (simply-laced) unitary quiver gauge theories. The Higgs branches of some unitary quivers are verified to give slices in the nilpotent cones of exceptional simple Lie algebras.

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arXiv2024

Orthosymplectic Quotient Quiver Subtraction

The technique of orthosymplectic quotient quiver subtraction is introduced. This involves subtraction of an orthosymplectic quotient quiver from a $3d\;\mathcal N=4$ orthosymplectic quiver gauge theory which has the effect of gauging subgroups of the IR Coulomb branch global symmetry. Orthosymplectic quotient quivers for $\mathrm{SU}(2),\;\mathrm{SU}(3),\;G_2,$ and $\mathrm{SO}(7)$ are found and derived from Type IIA brane systems involving negatively charged branes for certain $6d\;\mathcal N=(1,0)$ gauge theories. Orthosymplectic quotient quiver subtraction is applied to magnetic quivers for nilpotent orbit closures providing new orthosymplectic counterparts to known unitary quivers. New Coulomb branch constructions are found such as for two height four nilpotent orbit closures of $F_4$ and one of height three. A novel application is to find magnetic quivers and Type IIA brane systems for the $6d\;\mathcal N=(1,0)$ worldvolume theory of two $\frac{1}{2}$M5 branes probing $E_6$ Klein singularity and for $6d\;\mathcal N=(1,0)\;(E_6,E_6)$ conformal matter. These give a perturbative Lagrangian realisation to the dynamics of strongly interacting M5 branes. The magnetic quiver for $6d\;\mathcal N=(1,0)\;(E_6,E_6)$ conformal matter is star-shaped and can also be interpreted as a magnetic quiver for a class $\mathcal S$ theory specified by $\mathrm{SO}(26)$ algebra on a three-punctured sphere.

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arXiv2024

Quiver Polymerisation

Two new diagrammatic techniques on $3d\;\mathcal N=4$ quiver gauge theories, termed chain and cyclic quiver polymerisation are introduced. These gauge a diagonal $\mathrm{SU}/\mathrm{U}(k)$ subgroup of the Coulomb branch global symmetry of a quiver (or pair of quivers) with multiple legs. The action on the Coulomb branch is that of a $\mathrm{SU}/\mathrm{U}(k)$ hyper-K\"ahler quotient. The polymerisation techniques build and generalise known composition methods from class $\mathcal S$. Polymerisation is used to generate a wide range of magnetic quivers from various physical contexts. These include polymerisation constructions for Kronheimer-Nakajima quivers, which generalise the ADHM construction for the moduli space of $k\;\mathrm{SU}(N)$ instantons on $\mathbb C^2$ to A-type singularities. Also a polymerisation construction of the magnetic quiver for the $6d\;\mathcal N=(1,0)$ coming from two $\frac{1}{2}$ M5 branes probing an $E_6$ Klein singularity. We find a method of extending magnetic quivers for Class $\mathcal S$ theories to cure the incomplete Higgsing that arises when gluing punctures into the loops associated with higher genus theories. Other novel constructions include a unitary magnetic quiver for the closure of a height four nilpotent orbit of $\mathrm{SO}(7)$. We explore the relationships between the Coulomb and Higgs branches of quivers under polymerisation.

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arXiv2023

Actions on the quiver -- Discrete quotients on the Coulomb branch

This paper introduces two operations in quiver gauge theories. The first operation takes a quiver with a permutation symmetry $S_n$ and gives a quiver with adjoint loops. The corresponding 3d $\mathcal{N}=4$ Coulomb branches are related by an orbifold of $S_n$. The second operation takes a quiver with $n$ nodes connected by edges of multiplicity $k$ and replaces them by $n$ nodes of multiplicity $qk$. The corresponding Coulomb branch moduli spaces are related by an orbifold of type $\mathbb{Z}_q^{n-1}$. The first operation generalises known cases that appeared in the literature. These two operations can be combined to generate new relations between moduli spaces that are constructed using the magnetic construction.

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arXiv2023

Quotient Quiver Subtraction

We develop the diagrammatic technique of quiver subtraction to facilitate the identification and evaluation of the $\mathrm{SU}(n)$ hyper-K\"ahler quotient (HKQ) of the Coulomb branch of a $3d$ $\mathcal{N}=4$ unitary quiver theory. The target quivers are drawn from a wide range of theories, typically classified as ''good'' or ''ugly'', which satisfy identified selection criteria. Our subtraction procedure uses quotient quivers that are ''bad'', differing thereby from quiver subtractions based on Kraft-Procesi transitions. The procedure identifies one or more resultant quivers, the union of whose Coulomb branches corresponds to the desired HKQ. Examples include quivers whose Coulomb branches are moduli spaces of free fields, closures of nilpotent orbits of classical and exceptional type, and slices in the affine Grassmanian. We calculate the Hilbert Series and Highest Weight Generating functions for HKQ examples of low rank. For certain families of quivers, we are able to conjecture HWGs for arbitrary rank. We examine the commutation relations between quotient quiver subtraction and other diagrammatic techniques, such as Kraft-Procesi transitions, quiver folding, and discrete quotients.

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