Related papers: Crystal bases and three-dimensional $ \mathcal{N}=…

Obtaining the classification of 3d $\mathcal{N}=4$ quivers whose Coulomb branches have an isolated singularity is an essential step in understanding moduli spaces of vacua of supersymmetric field theories with 8 supercharges in any…

We study the representation theory of a quantum symmetric pair $(\mathbf{U},\mathbf{U}^{\jmath})$ with two parameters $p,q$ of type AIII, by using highest weight theory and a variant of Kashiwara's crystal basis theory. Namely, we classify…

To a quiver with involution, we study the Coulomb branch of the 3d $\mathcal{N} = 4$ involution-fixed part of the quiver gauge theory. We show that there is an algebra homomorphism from the corresponding shifted twisted Yangian to the…

We study two types of discrete operations on Coulomb branches of $3d$ $\mathcal{N}=4$ quiver gauge theories using both abelianisation and the monopole formula. We generalise previous work on discrete quotients of Coulomb branches and…

We propose a construction of the quantum-corrected Coulomb branch of a general 3d gauge theory with $\mathcal{N}=4$ supersymmetry, in terms of local coordinates associated with an abelianized theory. In a fixed complex structure, the…

Strong correlation effects in classical and quantum plasmas are discussed. In particular, Coulomb (Wigner) crystallization phenomena are reviewed focusing on one-component non-neutral plasmas in traps and on macroscopic two-component…

We show that Coulomb branches for $3$-dimensional $\mathcal{N}=4$ supersymmetric gauge theories have symplectic singularities. This confirms a conjecture of Braverman-Finkelberg-Nakajima.

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…

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…

This is a supplement to [arXiv:1503.03676], where an approach towards a mathematically rigorous definition of the Coulomb branch of a $3$-dimensional $\mathcal N=4$ SUSY gauge theory was proposed. We ask questions on their expected…

We give a crystal structure on the set of all irreducible components of Lagrangian subvarieties of quiver varieties. One con show that, as a crystal, it is isomorphic to the crystal base of an irreducible highest weight representation of a…

We study the vacuum structure of gauge theories with eight supercharges. It has been recently discovered that in the Higgs branch of $5d$ and $6d$ SQCD theories with eight supercharges, the new massless states, arising when the gauge…

Let $U_{q}^{-}(\mathfrak g)$ be the negative half of a quantum Borcherds-Bozec algebra $U_{q}(\mathfrak g)$ and $V(\lambda)$ be the irreducible highest weight module with $\lambda \in P^{+}$. In this paper, we investigate the structures,…

We present a new family of IR dualities in three space-time dimensions with eight supercharges. In contrast to 3d mirror symmetry, these dualities map Coulomb branches to Coulomb branches and Higgs branches to Higgs branches in the deep IR.…

We develop a classification of \emph{minimally unbalanced} $3d~\mathcal{N}=4$ quiver gauge theories. These gauge theories are important because the isometry group $G$ of their Coulomb branch contains a single factor, which is either a…

We study the Coulomb branches of three-dimensional $\mathcal N=4$ quiver gauge theories of type $T_\rho(SU(N))$ associated with non-maximal nilpotent orbits of $SL(N)$. Using the Hall--Littlewood closed form for Coulomb-branch Hilbert…

We introduce the shifted quantum affine algebras. They map homomorphically into the quantized $K$-theoretic Coulomb branches of $3d\ {\mathcal N}=4$ SUSY quiver gauge theories. In type $A$, they are endowed with a coproduct, and they act on…

For symmetric Kashiwara crystals of type $A$ and rank $e=2$, and for the canonical basis elements that we call external, corresponding to weights on the outer skin of the Kashiwara crystal, we construct the canonical basis elements in a…

We study the crystal base $\mathsf{B}(\infty)$ associated with the negative part of the quantum group for finite simple Lie algebras of types $E_6$ and $E_7$. We present an explicit description of $\mathsf{B}(\infty)$ as the image of a…

A distinctive duality present in 3d $\mathcal{N}=4$ theories is the 3d mirror symmetry. Under this duality, the Coulomb (Higgs) branch of one theory corresponds to the Higgs (Coulomb) branch of its mirror dual. This paper is divided into…