arXiv subjects

Deshuo Liu

Publications and source records attributed to Deshuo Liu.

6 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-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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arXiv2025

Interplay of Generalised Symmetries and Moduli Spaces in 3d $\mathcal{N}=5$ SCFTs

The moduli space and generalised global symmetries of 3d $\mathcal{N} = 5$ superconformal field theories are investigated, with a focus on the orthosymplectic ABJ theories and their discrete gauging variants. We extend the known classification of $\mathcal{N}=5$ moduli spaces as orbifolds $\mathbb{H}^{2N}/\Gamma$, where $\Gamma$ is a quaternionic reflection group, to theories incorporating $\mathrm{Spin}$, $\mathrm{O}^-$, and $\mathrm{Pin}$-type gauge groups. In these cases, we find that the moduli space is governed not by $\Gamma$ itself, but by a $\mathbb{Z}_2$ central extension thereof, for which we explicitly describe the generators. We provide a systematic method to construct the group $\Gamma'$ governing the moduli space of a theory $\mathcal{T}'$ obtained by gauging a $\mathbb{Z}_2$ zero-form symmetry of an original theory $\mathcal{T}$. This is achieved by identifying the specific generator that must be added to $\Gamma$. We compute the Hilbert series for these moduli spaces and verify them against the corresponding limits of the superconformal index, finding perfect agreement. We also discuss how 't Hooft anomalies for the zero-form symmetries manifest in the superconformal index and the moduli space. Furthermore, we revisit the symmetry category of the $\mathfrak{so}(2N)_{2k} \times \mathfrak{usp}(2N)_{-k}$ theories. Building on previous work that identified the symmetry category for all parities of $N$ and $k$, we provide the explicit symmetry webs for the opposite parity $D_8$ case. We find that the details of these webs differ from the previously studied $D_8$ webs corresponding to the both even parity case. Finally, we analyse theories with unequal ranks, those containing the $\mathfrak{so}(2N+1)$ gauge algebra, and the two SCFT variants based on the $F(4)$ superalgebra.

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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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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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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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