Related papers: Path-integral invariants in abelian Chern-Simons t…
We investigate the Reshetikhin--Turaev invariants associated to SU(2) for the 3-manifolds M obtained by doing any rational surgery along the figure 8 knot. In particular, we express these invariants in terms of certain complex double…
In this paper, the connection between the path integral representation of propagators in the coherent state basis with additional degrees of freedom \cite{rohwer} and the one without any such degrees of freedom \cite{sgfgs} is established.…
The proper action functional of (4k+3)-dimensional U(1)-Chern-Simons theory including the instanton sectors has a well known description: it is given on the moduli space of fields by the fiber integration of the cup product square of…
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…
The level-k U(1) Chern-Simons theory is a spin topological quantum field theory for k odd. Its dynamics is captured by the 2d CFT of a compact boson with a certain radius. Recently it was recognized that a dependence on the 2d spin…
In the works of A. Ach\'ucarro and P. K. Townsend and also by E. Witten, a duality between three-dimensional Chern-Simons gauge theories and gravity was established. In all cases, the results made use of the field equations. In a previous…
The abelian Chern-Simons theory is perturbed by introducing local gauge-invariant interaction terms depending on the curvature. The computation of the correlation function of two Wilson lines for two smooth closed nonintersecting curves is…
We recall the emergence of a generalized gauge theory from a noncommutative Riemannian spin manifold, viz. a real spectral triple $(A,H,D;J)$. This includes a gauge group determined by the unitaries in the $*$-algebra $A$ and gauge fields…
We use localization to compute the partition function of a four dimensional, supersymmetric, abelian gauge theory on a hemisphere coupled to charged matter on the boundary. Our theory has eight real supercharges in the bulk of which four…
We construct a 2+1 dimensional classical gauge theory on manifolds with spin structure whose action is a refinement of the Atiyah-Patodi- Singer eta-invariant for twisted Dirac operators. We investigate the properties of the Lagrangian…
By incorporating two gauge connections, transgression forms provide a generalization of Chern-Simons actions that are genuinely gauge-invariant on bounded manifolds. In this work, we show that, when defined on a manifold with a boundary,…
This is the first of a series of papers in which we introduce and study a rigorous "simplicial" realization of the non-Abelian Chern-Simons path integral for manifolds M of the form M = Sigma x S1 and arbitrary simply-connected compact…
We explicitly determine the symplectic structure on the phase space of Chern-Simons theory with gauge group $G\ltimes g^*$ on a three-manifold of topology $R \times S$, where $S$ is a surface of genus $g$ with $n+1$ punctures. At each…
We define a sequence of invariants $\mathcal{Z}_{N}^{\psi}$ of tangles with flat $\mathfrak{sl}_{2}$ connections (i.e. hyperbolic structures) on their complements. These can be interpreted as a geometric twist of the Kashaev invariant or as…
N = 6 superconformal Chern-Simons theory was proposed as gauge theory dual to Type IIA string theory on AdS4*CP3. We study integrability of the theory from conformal dimension spectrum of single trace operators at planar limit. At strong `t…
We extend the Chern-Simons perturbative invariant of Axelrod and Singer to non-acyclic connections. We construct a solution of the quantum master equation on the space of functions on the cohomology of the connection. We prove that this…
The first part of this text is a gentle exposition of some basic constructions and results in the extended prequantum theory of Chern-Simons-type gauge field theories. We explain in some detail how the action functional of ordinary 3d…
N=6 superconformal Chern-Simons theory with gauge group U(M)xU(N)} is dual to N M2-branes and (M-N) fractional M2-branes, equivalently, discrete 3-form holonomy at C4/Zk orbifold singularity. We show that, much like its regular counterpart…
In a previous paper [\AS], we used superspace techniques to prove that perturbation theory (around a classical solution with no zero modes) for Chern--Simons quantum field theory on a general $3$-manifold $M$ is finite. We conjectured (and…
We propose a unifying theory for both the integral and fractional quantum Hall regimes. This theory reconciles the Finkelstein approach to localization and interaction effects with the topological issues of an instanton vacuum and…