Related papers: Vortices and Vermas
We find the perturbative potential on the 3d $\mathcal{N}\!=\!2$ Coulomb branch arising from a chiral 4d $\mathcal{N}\!=\!1$ gauge theory on $\mathbb{R}^3 \times S^1$, zeta-regularizing the D-term couplings generated by the Kaluza-Klein…
Given a finite set E and an operator sigma:2^{E}-->2^{E}, two subsets X,Y of the ground set E are cospanning if sigma(X)=sigma(Y) (Korte, Lovasz, Schrader; 1991). We investigate cospanning relations on violator spaces. A notion of a…
We define the oscillator and Coulomb systems on four-dimensional spaces with U(2)-invariant Kahler metric and perform their Hamiltonian reduction to the three-dimensional oscillator and Coulomb systems specified by the presence of Dirac…
We examine two nonselfadjoint operator algebras: the weighted shift algebra, and the Volterra operator algebra. In both cases, the operator algebra is the norm closure of the polynomials in the operator norm. In the case of the weighted…
We study Rota--Baxter operators on vertex algebras using the integrated $\lambda$-bracket formalism. A Rota--Baxter operator produces a deformed vertex algebra structure, and the difference between the deformed and original brackets yields…
We construct actions for (p,0)- and (p,1)- supersymmetric, 1 <= p <= 4, two-dimensional gauge theories coupled to non-linear sigma model matter with a Wess-Zumino term. We derive the scalar potential for a large class of these models. We…
We present a formula for the Hilbert series that counts gauge invariant chiral operators in a large class of 3d ${\cal N} \ge 2$ Yang-Mills-Chern-Simons theories. The formula counts 't Hooft monopole operators dressed by gauge invariants of…
We show that the algebra $D_\hbar(SL_n/U)$ of differential operators on the base affine space of $SL_n$ is the quantized Coulomb branch of a certain 3d $\mathcal{N} = 4$ quiver gauge theory. In the semiclassical limit this proves a…
The monopole systems with hidden symmetry of the two-dimensional Coulomb problem are considered. One of them, the "charge-charged magnetic vortex" with a half-spin, is constructed by reducing the quantum circular oscillator with respect to…
The supersymmetric cigar (half-)index or cigar partition function of 3d $\mathcal{N}=2$ gauge theories contains a wealth of information. Physically, it captures the spectrum of BPS states, the non-perturbative corrections to various…
We construct the most general disorder operator for SU(N) lattice gauge theory in $(2+1)$ dimension by using exact duality transformations. These disorder operators, defined on the plaquettes and characterized by ($\text{N}-1$) angles, are…
In this article we analyze a two dimensional lattice gauge theory based on a quantum group.The algebra generated by gauge fields is the lattice algebra introduced recently by A.Yu.Alekseev,H.Grosse and V.Schomerus we define and study wilson…
We construct the world-volume action of a probe D3-brane in $AdS_5 \times S^5$ with $N$ units of flux. It has the field content, symmetries, and dualities of the $U(1)$ factor of ${\cal N} =4$ $U(N+1)$ super Yang--Mills theory,…
Given a representation N of a reductive group G, Braverman-Finkelberg-Nakajima have defined a remarkable Poisson variety called the Coulomb branch. Their construction of this space was motivated by considerations from 3d gauge theories and…
Aspects of three dimensional $\mathcal{N}=2$ gauge theories with monopole superpotentials and their dualities are investigated. The moduli spaces of a number of such theories are studied using Hilbert series. Moreover, we propose new…
We consider perturbations of dynamical semigroups on the algebra of all bounded operators in a Hilbert space generated by covariant completely positive measures on the semi-axis. The construction is based upon unbounded linear perturbations…
We revisit the vacuum structure of the $\mathcal{N}=1$ Intriligator-Seiberg-Shenker model on $\mathbb{R}^3\times S^1$. Guided by the Cardy-like asymptotics of its Romelsberger index, and building on earlier semi-classical results by Poppitz…
The vortex solutions of various classical planar field theories with (Abelian) Chern-Simons term are reviewed. Relativistic vortices, put forward by Paul and Khare, arise when the Abelian Higgs model is augmented with the Chern-Simons term.…
The presence of magnetic monopole like excitations of nonabelian varieties is one of the subtlest consequences of spontaneously broken gauge symmetries. Important hints about their quantum mechanical properties, which remained long…
A new functional calculus, developed recently for a fully non-perturbative treatment of quantum gravity, is used to begin a systematic construction of a quantum theory of geometry. Regulated operators corresponding to areas of 2-surfaces…