Related papers: Perturbative Chern-Simons invariants from non-acyc…
We discretize Chern-Simons couplings in gauge invariant way. We obtain (p+q)-forms representing Chern-Simons couplings on (p + q)-simplexes from wedge products of p- and q-forms on p- and q-simplexes, respectively, where p- and q-simplexes…
We present basic constructions and properties in arithmetic Chern-Simons theory with finite gauge group along the line of topological quantum field theory. For a finite set $S$ of finite primes of a number field $k$, we construct arithmetic…
We give a formula of 3-dimensional invariant for a cyclic contact branched covering of the standard contact S^{3}.
The spacetime symmetries of classical electrodynamics supplemented with a Chern-Simons term that contains a constant nondynamical 4-vector are investigated. In addition to translation invariance and the expected three remaining Lorentz…
We prove a general local rigidity theorem for pull-backs of homogeneous forms on reductive symmetric spaces under representations of discrete groups. One application of the theorem is that the volume of a closed manifold locally modelled on…
In this work we review various findings in the planar quantum physics with the special emphasis on the two-component quantum electrodynamics in three-dimensional spacetime (QED_{3}) with the Chern-Simons (CS) term. First the classical…
We consider the Gopakumar-Ooguri-Vafa correspondence, relating ${\rm U}(N)$ Chern-Simons theory at large $N$ to topological strings, in the context of spherical Seifert 3-manifolds. These are quotients $\mathbb{S}^{\Gamma} =…
We study an important property of shape invariant supersymmetric quantum mechanical systems. Particularly, we demonstrate that each shape invariant supersymmetric system can constitute a $Z_3$-graded topological symmetric algebra. The…
We study three-dimensional superconformal field theories on wrapped M5-branes. Applying the gauge/gravity duality and the recently proposed 3d-3d relation, we deduce quantitative predictions for the perturbative free energy of a…
This paper is devoted to the construction of differential geometric invariants for the classification of "Quaternionic" vector bundles. Provided that the base space is a smooth manifold of dimension two or three endowed with an involution…
It has been folklore for several years in the knot theory community that certain integrals on configuration space, originally motivated by perturbation theory for the Chern-Simons field theory, converge and yield knot invariants. This was…
In this paper we construct a topological model for the Witten-Reshetikhin-Turaev invariants for $3$-manifolds coming from the quantum group $U_q(sl(2))$, as graded intersection pairings of homology classes in configuration spaces. More…
The general structure of the perturbative expansion of the vacuum expectation value of a Wilson line operator in Chern-Simons gauge field theory is analyzed. The expansion is organized according to the independent group structures that…
The path integral for the partition function of Chern-Simons gauge theory with a compact gauge group is evaluated on a general Seifert 3-manifold. This extends previous results and relies on abelianisation, a background field method and…
We investigate the covariant formulation of Chern-Simons theories in a general odd dimension which can be obtained by introducing a vacuum connection field as a reference. Field equations, Noether currents and superpotentials are computed…
We study the physics of multiple M5-branes compactified on a hyperbolic 3-manifold. On the one hand, it leads to the 3d-3d correspondence which maps an $\mathcal{N}=2$ superconformal field theory to a pure Chern-Simons theory on the…
We determine perturbatively the conformal manifold of N=2 Chern-Simons matter theories with the aim of checking in the three dimensional case the general prescription based on global symmetry breaking, recently introduced. We discuss in…
A Chern-Simons theory in 11 dimensions, which is a piece of the 11 dimensional supergravity action, is considered as a quantum field theory in its own right. We conjecture that it defines a non-perturbative phase of M theory in which the…
Earlier results show that the N = 1/2 supersymmetric path integral on a closed even dimensional Riemannian spin manifold (X,g) can be constructed in a mathematically rigorous way via Chen differential forms and techniques from…
We summarize the progress made during the last few years on the study of Vassiliev invariants from the point of view of perturbative Chern-Simons gauge theory. We argue that this approach is the most promising one to obtain a combinatorial…