相关论文: Coulomb Branch Quantization and Abelianized Monopo…

Monopole bubbling contributions to supersymmetric 't Hooft loops in 4d $\mathcal{N}=2$ theories are computed by SQM indices. As recently argued, those indices are hard to compute due to the presence of Coulomb vacua that are not captured by…

I give a simple construction of certain Coulomb branches $C_{3,4}(G;E)$ of gauge theory in 3 and 4 dimensions defined by Nakajima et al. for a compact Lie group $G$ and a polarisable quaternionic representation $E$. The manifolds $C(G; 0)$…

The Coulomb branch of 3-dimensional N=4 gauge theories is the space of bare and dressed BPS monopole operators. We utilise the conformal dimension to define a fan which, upon intersection with the weight lattice of a GNO-dual group, gives…

For a noncommutative algebra $\mathcal{A}$ and an antilinear automorphism $\rho$ of $\mathcal{A}$, there is a notion of a positive trace. When we have a three-dimensional $\mathcal{N}=4$ gauge theory or four-dimensional $\mathcal{N}=2$…

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…

This paper addresses a long standing problem - to identify the chiral ring and moduli space (i.e. as an algebraic variety) on the Coulomb branch of an N = 4 superconformal field theory in 2+1 dimensions. Previous techniques involved a…

We study the Coulomb branches of $3d$ $\mathcal{N}=4$ quiver gauge theories, focusing on the generators for their quantized coordinate rings. We show that there is a surjective map from a shifted Yangian onto the quantized Coulomb branch,…

In recent work, we demonstrated that a spectral variety for the Berry connection of a 2d $\mathcal{N}=(2,2)$ GLSM with K\"ahler vacuum moduli space $X$ and abelian flavour symmetry is the support of a sheaf induced by a certain action on…

We analyze the coulomb branch of the non-unitary Lorentzian three algebra theory that has been proposed as a possible candidate for describing the world volume theory of multiple M2-branes. In order that it describes the theory of multiple…

We use brane techniques to study the space of vacua of abelian 3d $\mathcal{N}=3$ gauge theories. The coordinates on these spaces are the vevs of chiral monopole and meson operators, which are realized in the type IIB brane configuration of…

We generalize the mathematical definition of Coulomb branches of $3$-dimensional $\mathcal N=4$ SUSY quiver gauge theories in arXiv:1503.03676, arXiv:1601.03686, arXiv:1604.03625 to the cases with symmetrizers. We obtain generalized affine…

According to the proposal of Hanany and Witten, Coulomb branches of N=4 SU(n) gauge theories in three dimensions are isometric to moduli spaces of BPS monopoles. We generalize this proposal to gauge theories with matter, which allows us to…

We present an algorithm to extract the Coulomb branch Hasse diagram of orthosymplectic 3d $\mathcal{N}=4$ quiver gauge theories. The algorithm systematically predicts all descendant theories arising from Coulomb branch Higgsing, thereby…

Let $A=A_{G,N}^{\hbar=1}$ be a quantized Coulomb branch with an antilinear automorphism $\rho$. A map $T\colon A\to\mathbb{C}$ is called a positive trace if $T(a\rho(a))>0$ for all nonzero $a\in A$. Positive traces on Coulomb branches…

We study monopole operators at the infrared fixed points of Abelian and non-Abelian gauge theories with N_f fermion flavors in three dimensions. At large N_f, independent monopole operators can be defined via the state-operator…

We study some topological aspects of non-abelian gauge theories intimately connected to the Lie algebras of the gauge groups and the homotopy theory in the generalized gauge orbit space. The physics connection to the non-perturbative…

We present a new family of dualities for three-dimensional gauge theories, motivated by the brane realization of the reduction of four-dimensional dualities on a circle. This family can be understood as a generalization of Aharony duality…

Quiver quantum mechanics describes the low energy dynamics of a system of wrapped D-branes. It captures several aspects of single and multicentered BPS black hole geometries in four-dimensional $\mathcal{N} = 2$ supergravity such as the…

These are (somewhat informal) lectures notes for the CIME summer school "Geometric Representation Theory and Gauge Theory" in June 2018. In these notes we review the results and constructions of a series of our joint papers with H.Nakajima…

This is a companion paper of arXiv:1601.03586. We study Coulomb branches of unframed and framed quiver gauge theories of type $ADE$. In the unframed case they are isomorphic to the moduli space of based rational maps from ${\mathbb C}P^1$…