arXiv subjects

Guhesh Kumaran

Publications and source records attributed to Guhesh Kumaran.

9 recordsLinked to original sources

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-Kähler 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-Kähler quotient) of an $\mathrm{Sp}(1)\times\mathrm{O}(1)$ gauge theory.

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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

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

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

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-Kähler 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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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

Quotient Quiver Subtraction

We develop the diagrammatic technique of quiver subtraction to facilitate the identification and evaluation of the $\mathrm{SU}(n)$ hyper-Kähler 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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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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