Related papers: On refined Chern-Simons and refined ABJ matrix mod…
The Chern-Simons (CS) theory in three dimensions with a compact gauge group G is studied. Starting from the BRST quantization of the theory defined in R^3, the values of gauge invariants observables are computed in any closed and orientable…
We consider Chern-Simons theory with complex gauge group and present a complete non-perturbative evaluation of the path integral (the partition function and certain expectation values of Wilson loops) on Seifert fibred 3-Manifolds. We use…
Mixed anomalies, higher form symmetries, two-group symmetries and non-invertible symmetries have proved to be useful in providing non-trivial constraints on the dynamics of quantum field theories. We study mixed anomalies involving discrete…
We show that baryon-like operators exist in the N=6 superconformal Chern-Simons-matter theory constructed by Aharony, Bergman, Jafferis and Maldacena (ABJM). This involves the introduction of Wilson(or 't Hooft) lines ending on baryon-like…
$q,t$-deformed matrix models give rise to representations of the deformed Virasoro algebra and more generally of the quantum toroidal $\mathfrak{gl}_1$ algebra. These representations are described in terms of finite difference equations…
We calculate the superconformal index for N=6 Chern-Simons-matter theory with gauge group U(N) X U(N) at arbitrary allowed value of the Chern-Simons level k. The calculation is based on localization of the path integral for the index. Our…
We construct and study a new topological field theory in three dimensions. It is a hybrid between Chern-Simons and Rozansky-Witten theory and can be regarded as a topologically-twisted version of the N=4 d=3 supersymmetric gauge theory…
We study light-like polygonal Wilson loops in three-dimensional Chern-Simons and ABJM theory to two-loop order. For both theories we demonstrate that the one-loop contribution to these correlators cancels. For pure Chern-Simons, we find…
This work identifies the Reshetikhin-Turaev invariant of links in terms of a trace map on factorization homology. In particular, to recover the knot invariants associated to Chern-Simons theories, we construct a filtered…
We study partition functions of 3d $\mathcal{N}=2$ U(N) gauge theories on compact manifolds which are $S^1$ fibrations over $S^2$. We show that the partition functions are free field correlators of vertex operators and screening charges of…
We use group theoretic methods to calculate the spectrum of short multiplets around the extremum of N=8 gauged supergravity potential which possesses N=2 supersymmetry and SU(3) global symmetry. Upon uplifting to M-theory, it describes a…
The Langmann-Szabo-Zarembo (LSZ) matrix model is a complex matrix model with a quartic interaction and two external matrices. The model appears in the study of a scalar field theory on the non-commutative plane. We prove that the LSZ matrix…
In this paper we continue the study of the superconformal index of four-dimensional $\mathcal{N}=2$ theories of class $\mathcal{S}$ in the presence of surface defects. Our main result is the construction of an algebra of difference…
We characterise the quantum group gauge symmetries underlying q-deformations of two-dimensional Yang-Mills theory by studying their relationships with the matrix models that appear in Chern-Simons theory and six-dimensional N=2 gauge…
We study Chern-Simons Gauge Theory in axial gauge on ${\mathbb R}^3.$ This theory has a quadratic Lagrangian and therefore expectations can be computed nonperturbatively by explicit formulas, giving an (unbounded) linear functional on a…
Reshetikhin-Turaev (a.k.a. Chern-Simons) TQFT is a functor that associates vector spaces to two-dimensional genus g surfaces and linear operators to automorphisms of surfaces. The purpose of this paper is to demonstrate that there exists a…
The fusion ring for $\widehat{\mathfrak{su}}(n)_m$ Wess-Zumino-Witten conformal field theories is known to be isomorphic to a factor ring of the ring of symmetric polynomials presented by Schur polynomials. We introduce a deformation of…
We study issues concerning perturbative integrability of N=6 Chern-Simons theory at planar and weak `t Hooft coupling regime. By Feynman diagrammatics, we derive so called maximal-ranged interactions in the quantum dilatation generator,…
We propose an SL(2,R) Chern-Simons description of Liouville field theory (LFT), whose correlation function duals to partition function of N=2 SU(2) gauge theories. We give the dual expressions for conformal blocks, fusion rules, and Wilson…
We first construct an action of the extended double affine braid group $\mathcal{\ddot{B}}$ on the quantum toroidal algebra $U_{q}(\mathfrak{g}_{\mathrm{tor}})$ in untwisted and twisted types. As a crucial step in the proof, we obtain a…