Related papers: 't Hooft lines of ADE-type and Topological Quivers
We study 't Hooft lines and the associated $\mathcal{L}$- operators in topological 4D Chern-Simons theory with gauge symmetry given by the exceptional groups E$_{6}$ and E$_{7}$. We give their oscillator realisations and propose topological…
We study 't Hooft lines in four-dimensional holomorphic-topological Chern-Simons theory. We relate them to Q-operators in the theory of integrable systems. We give a physical interpretation of the fundamental TQ and QQ relations satisfied…
We study the properties of interacting line defects in the four-dimensional Chern Simons (CS) gauge theory with invariance given by the $SL\left( m|n\right) $ super-group family. From this theory, we derive the oscillator realisation of the…
As a generalisation of the correspondence linking 2D integrable systems with 4D Chern-Simons (CS) gauge theory, superspin chains are realized by means of crossing electric and magnetic super line defects in the 4D CS with super gauge…
We establish a correspondence between a class of Wilson-'t Hooft lines in four-dimensional $\mathcal{N} = 2$ supersymmetric gauge theories described by circular quivers and transfer matrices constructed from dynamical L-operators for…
Using 4D Chern-Simons (CS) theory with gauge symmetry $G$ having minuscule coweights, we develop a suitable operator basis to deal with the explicit calculation of the Lax operator of integrable spin chain satisfying the RLL equation. Using…
These notes are intended to be a pedagogical introduction to higher-form symmetries, which are symmetries whose charged objects are extended operators supported on lines, surfaces, and etc. This subject has been one of the most popular and…
We explore higher-form symmetries of M- and F-theory compactified on elliptic fibrations, determined by the topology of their asymptotic boundaries. The underlying geometric structures are shown to be equivalent to known characterizations…
This is the sixth article in the collection of reviews "Exact results on N=2 supersymmetric gauge theories", ed. J.Teschner. It is discussed how to use localisation techniques for the calculation of expectation values of Wilson and 't Hooft…
In $3d$ Chern-Simons theory, there is a discrete one-form symmetry, whose symmetry group is isomorphic to the center of the gauge group. We study the 't Hooft anomaly associated to this discrete one-form symmetry in theories with generic…
We consider the defect CFT defined by a 't Hooft line embedded in N=4 super Yang-Mills theory. By explicitly quantizing around the given background we exactly reproduce a prediction from S-duality for the correlators between the 't Hooft…
We present a conjecture for the crossing symmetry rules for Chern-Simons gauge theories interacting with massive matter in $2+1$ dimensions. Our crossing rules are given in terms of the expectation values of particular tangles of Wilson…
We consider 4-dimensional $\mathcal{N} = 2$ superconformal quiver theories with $SU(N)^M$ gauge group and bi-fundamental matter and we evaluate correlation functions of $n$ coincident Wilson loops in the planar limit of the theory.…
't Hooft anomalies impose fundamental constraints on quantum matter and often lead to emergent symmetry structures upon gauging. We analyze a lattice model with four global symmetries realizing a mixed anomaly described by $\sim a_1\wedge…
Kapustin-Witten (KW) equations are encountered in the localization of the topological N=4 SYM theory. Mikhaylov has constructed model solutions of KW equations for the boundary 't~Hooft operators on a half space. Direct proof of the…
We explore the connection between the global symmetry quantum numbers of line defects and 't Hooft anomalies. Relative to local (point) operators, line defects may transform projectively under both internal and spacetime symmetries. This…
We consider $\mathcal{N}=2$ superconformal quiver gauge theories in four dimensions and evaluate the chiral/anti-chiral correlators of single-trace operators. We show that it is convenient to form particular twisted and untwisted…
The 't Hooft expansion of SU(N) Chern-Simons theory on $S^3$ is proposed to be exactly dual to the topological closed string theory on the $S^2$ blow up of the conifold geometry. The $B$-field on the $S^2$ has magnitude $Ng_s=\lambda$, the…
The Hilbert space of level $q$ Chern-Simons theory of gauge group $G$ of the ADE type quantized on $T^2$ can be represented by points that lie on the weight lattice of the Lie algebra $\mathfrak{g}$ up to some discrete identifications. Of…
We investigate the planar solution of matrix models derived from various Chern-Simons-matter theories compatible with the planar limit. The saddle-point equations for most of such theories can be solved in a systematic way. A relation to…