Related papers: A Wilson Line Realisation of Quantum Groups
Charge and magnetic flux bearing operators are introduced in Chern-Simons theory both in its pure form and when it is coupled to fermions. The magnetic flux creation operator turns out to be the Wilson line. The euclidean correlation…
Wilson line on a non-simply connected manifold is a nice way to break SU(5) unified symmetry, and to solve the doublet--triplet splitting problem. This mechanism also requires, however, that the two Higgs doublets are strictly vector-like…
Non-perturbative aspects of $\mathcal{N}=2$ supersymmetric gauge theories of class $\mathcal{S}$ are deeply encoded in the algebra of functions on the moduli space $\mathcal{M}_\text{flat}$ of flat $SL(N)$-connections on Riemann surfaces.…
A brief review of a self-contained genuinely three-dimensional monodromy-matrix based non-perturbative covariant path-integral approach to {\it polynomial invariants} of knots and links in the framework of (topological) quantum Chern-Simons…
In the late 1980s Witten used the Chern-Simons form of a connection to construct new invariants of 3-manifolds and knots, recovering in particular the Jones invariants. Since then the associated topological quantum field theory (TQFT) has…
We present an analysis of the canonical structure of the WZW theory with untwisted conformal boundary conditions. The phase space of the boundary theory on a strip is shown to coincide with the phase space of the Chern-Simons theory on a…
Over the years, many theoretical frameworks have been developed to understand the remarkable physics of the quantum Hall system. In this work we discuss the interplay among quantum wires, Chern-Simons theory, bosonization, and…
Chern-Simons (CS) theories with rank $N$ and level $k$ on Seifert manifold are discussed. The partition functions of such theories can be written as a function of modular transformation matrices summed over different integrable…
In this paper we investigate the large-$N$ behavior of 5-dimensional $\mathcal{N}=1$ super Yang-Mills with a level $k$ Chern-Simons term and an adjoint hypermultiplet. As in three-dimensional Chern-Simons theories, one must choose an…
We examine Chern-Simons theory as a deformation of a 3-dimensional BF theory that is partially holomorphic and partially topological. In particular, we introduce a novel gauge that leads naturally to a one-loop exact quantization of this BF…
We revisit and clarify some aspects of perturbative renormalization in pure Chern-Simons theory by means of a localization principle associated with an underlying supersymmetry. This perspective allows the otherwise perturbative one-loop…
We apply the mechanism of factorization homology to construct and compute category-valued two-dimensional topological field theories associated to braided tensor categories, generalizing the $(0,1,2)$-dimensional part of…
Intertwined multiple Chern-Simons gauge fields induce matrix statistics among particles. We analyse this theory on a torus, focusing on the vacuum structure and the Hilbert space. The theory can be mimicked, although not completely, by an…
Using localization technique, we calculate the partition function and the expectation value of Wilson loop operator in Chern-Simons theory on general lens spaces L(p,q)(including S2XS1). Our results are consistent with known results.
We show how to incorporate massive spinning fields into the Euclidean path integral of three-dimensional quantum gravity via its Chern-Simons formulation. The coupling of the spinning fields to gravity is captured by a Wilson spool, a…
Quiver gauge theories with a large number of nodes host a wealth of Wilson loop operators. Expectation values are obtained, using supersymmetric localization, for Wilson loops in the antisymmetric representations associated with each…
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…
In this paper, we present a systematic study of the Chern--Simons theory with gauge group \(\mathrm{SL}(2,\mathbb{R})\times\mathrm{SL}(2,\mathbb{R})\) restricted to a wedge-identified manifold in the hyperbolic upper-half-space. The wedge…
A general formula for physical observables in Chern-Simons theory with an arbitrary compact Lie group $G$, on an arbitrary closed oriented three-dimensional manifold $\cM$ is derived in terms of vacuum expectation values of Wilson loops in…
We construct a family of 3d quantum field theories $\mathcal T_{n,k}^A$ that conjecturally provide a physical realization -- and derived generalization -- of non-semisimple mathematical TQFT's based on the modules for the quantum group…