Related papers: A note on universality in refined Chern-Simons the…
We propose a simple abstract version of Calderon--Zygmund theory, which is applicable to spaces with exponential volume growth, and then show that amenable Lie groups can be treated within this framework.
We formulate and prove a twofold generalisation of Lie's second theorem that integrates homomorphisms between formal group laws to homomorphisms between Lie groups. Firstly we generalise classical Lie theory by replacing groups with…
We present a general approach to construct a class of generalized topological field theories with constraints by means of generalized differential calculus and its application to connection theory. It turns out that not only the ordinary BF…
General relativity is extended by promoting the three-dimensional gravitational Chern-Simons term to four dimensions. This entails choosing an embedding coordinate v_\mu -- an external quantity, which we fix to be a non-vanishing constant…
The Coulomb branch indices of Argyres-Douglas theories on $L(k,1)\times S^{1}$ are recently identified with matrix elements of modular transforms of certain $2d$ vertex operator algebras in a particular limit. A one parameter generalization…
We give a very simple proof that the renormalization of the Chern-Simons coupling in the Wilsonian effective action is exhausted at one-loop. Our proof can apply to arbitrary 2+1-dimensional abelian as well as nonabelian gauge theories…
We prove that the Voronin universality theorem for the Riemann zeta-function extends to the line Re(s)=1 if in addition to vertical shifts we also allow scaling and adding a sufficiently large constant.
We study a one-dimensional toy version of the Chern-Simons theory. We construct its simplicial version which comprises features of a low-energy effective gauge theory and of a topological quantum field theory in the sense of Atiyah.
For simple Lie algebras we construct characteristic identities for split (polarized) Casimir operators in representations $T \otimes Y_n$ and $T \otimes Y_n'$, where $T$ -- defining (minimal fundamental for exceptional Lie algebras)…
We extend Riemann's rearrangement theorem on conditionally convergent series of real numbers to multiple instead of simple sums.
Motivated by a recent paper of Fock and Rosly \cite{FoRo} we describe a mathematically precise quantization of the Hamiltonian Chern-Simons theory. We introduce the Chern-Simons theory on the lattice which is expected to reproduce the…
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…
A brief introduction to Topological Quantum Field Theory as well as a description of recent progress made in the field is presented. I concentrate mainly on the connection between Chern-Simons gauge theory and Vassiliev invariants, and…
The three dimensional Chern-Simons theory on $\rr^2_{\theta}\times \rr$ is studied. Considering the gauge transformations under the group elements which are going to one at infinity, we show that under arbitrary (finite) gauge…
A simple cubic matrix model is presented, which has truncations that, it is argued, lead at the classical level to a variety of theories of gauge fields and gravity. These include Chern-Simons theory in d=3, and BF theory and general…
The theory of Weil-Stark elements is used to develop an axiomatic approach to the formulation of refined versions of Stark's Conjecture. This gives concrete new results concerning leading terms of Artin $L$-series and arithmetic properties…
We prove a discretized Product Theorem for general simple Lie groups, in the spirit of Bourgain's Discretized Sum-Product Theorem.
A novel approach to the analysis of a noncommutative Chern--Simons gauge theory with matter coupled in the adjoint representation has been discussed. The analysis is based on a recently proposed closed form Seiberg--Witten map which is…
We present the universal, in Vogel's sense, expression for the quantum dimension of Cartan product of an arbitrary number of adjoint and $X_2$ representations of simple Lie algebras. The same formula mysteriously gives quantum dimensions of…
Various applications of Chern-Simons theory in algebraic topology, in particular knot theory, condensed matter physics and cosmology are reviewed. Special attention is paid to appearances of Chern-Simons actions in the theory of the…