Related papers: Reshetikhin-Turaev construction and $\mathrm{U}(1)…
In this article we show that the use of Deligne-Beilinson cohomology in the context of the $U(1)$ BF theory on a closed 3-manifold $M$ yields a discrete $\Z_N$ BF theory whose partition function is an abelian TV invariant of $M$. By…
The issue of how to deal with the modular transformations -- large diffeomorphisms -- in (2+1)-quantum gravity on the torus is discussed. I study the Chern-Simons/connection representation and show that the behavior of the modular…
A U(N) Chern-Simons theory on noncommutative $\mathbb{R}^{3}$ is constructed as a $\q$-deformed field theory. The model is characterized by two symmetries: the BRST-symmetry and the topological linear vector supersymmetry. It is shown that…
We consider the Chern-Simons theory with Wilson lines in 3D and in 1D in the BV-BFV formalism of Cattaneo-Mnev-Reshetikhin. In particular, we allow for Wilson lines to end on the boundary of the space-time manifold. In the toy model of 1D…
We study Chern-Simons theory on 3-manifolds M that are circle-bundles over 2-dimensional orbifolds S by the method of Abelianisation. This method, which completely sidesteps the issue of having to integrate over the moduli space of…
The superspace geometry of Chern-Simons forms is shown to be closely related to that of the 3-form multiplet. This observation allows to simplify considerably the geometric structure of supersymmetric Chern-Simons forms and their coupling…
We consider N = 3 supersymmetric Chern-Simons gauge theories with product unitary and orthosymplectic groups and bifundamental and fundamental fields. We study the partition functions on an S^3 by using the Kapustin-Willett-Yaakov matrix…
We construct a topological Chern-Simons sigma model on a Riemannian three-manifold M with gauge group G whose hyperkahler target space X is equipped with a G-action. Via a perturbative computation of its partition function, we obtain new…
We consider the geometric quantisation of Chern--Simons theory for closed genus-one surfaces and semisimple complex groups. First we introduce the natural complexified analogue of the Hitchin connection in K\"{a}hler quantisation, with…
This article studies the nonabelian localization results of Beasley and Witten, and considers the analogue of these results when the gauge group is U(1). It compares these results with results of Manoliu on abelian Chern-Simons theory,…
We show that the Reshetikhin-Turaev-Walker invariant of 3-manifolds can be normalized to obtain an invariant of 4-dimensional thickenings of 2-complexes. Moreover when the underlying semisimple tortile category comes from the…
A modular tensor category $\mathcal{C}$ gives rise to a Reshetikhin-Turaev type topological quantum field theory which is defined on 3-dimensional bordisms with embedded $\mathcal{C}$-coloured ribbon graphs. We extend this construction to…
We show in this paper that Abelian Chern-Simons term is induced in 2+1 and 3+1 dimensional rotating superfluid $^{3}$He-A and plays important roles in its dynamics. Because U(1) symmetry is spontaneously broken in $^{3}$He-A, Goldstone mode…
In this article we exploit Ruelle-type spectral functions and analyze the Verma module over Virasoro algebra, boson-fermion correspondence, the analytic torsion, the Chern-Simons and $\eta$ invariants, as well as the generation function…
U(1) Chern-Simons theory is quantized canonically on manifolds of the form $M=\mathbb{R}\times\Sigma$, where $\Sigma$ is a closed orientable surface. In particular, we investigate the role of mapping class group of $\Sigma$ in the process…
We develop several methods that allow us to compute all-loop partition functions in perturbative Chern-Simons theory with complex gauge group G_C, sometimes in multiple ways. In the background of a non-abelian irreducible flat connection,…
For each integral homology sphere $Y$, a function $\Gamma_Y$ on the set of integers is constructed. It is established that $\Gamma_Y$ depends only on the homology cobordism of $Y$ and it recovers the Fr{\o}yshov invariant. A relation…
We perform a resurgence analysis of the $SU(2)$ Chern-Simons partition function on a Brieksorn homology sphere $\Sigma(2,5,7)$. Starting from an exact Chern-Simons partition function, we study the Borel resummation of its perturbative…
With the goal of constructing the supersymmetric action for all fields, massless and massive, obtained by Kaluza-Klein compactification from type II theory or M-theory in a closed form, we embed the (Abelian) tensor hierarchy of p-forms in…
Invariants for framed links in $S^3$ obtained from Chern-Simons gauge field theory based on an arbitrary gauge group (semi-simple) have been used to construct a three-manifold invariant. This is a generalization of a similar construction…