Related papers: Arithmetic Chern-Simons Theory II

We consider topological field theories that compute the Reidemeister-Milnor-Turaev torsion in three dimensions. These are the psl(1|1) and the U(1|1) Chern-Simons theories, coupled to a background complex flat gauge field. We use the 3d…

In temporal gauge A_{0}=0 the 3d Chern-Simons theory acquires quadratic action and an ultralocal propagator. This directly implies a 2d R-matrix representation for the correlators of Wilson lines (knot invariants), where only the crossing…

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…

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…

Reducing a 3-dimensional Chern-Simons term by a symmetry yields other topologically interesting structures. Specifically, reducing by radial symmetry results in a 1-dimensional quantum mechanical model, which has recently been used in an…

Certain two dimensional topological field theories can be interpreted as string theory backgrounds in which the usual decoupling of ghosts and matter does not hold. Like ordinary string models, these can sometimes be given space-time…

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…

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 recent developments in the study of topological multi-boundary entanglement in the context of 3d Chern-Simons theory (with gauge group $G$ and level $k$) suggest a strong interplay between entanglement measures and number theory. The…

We discuss a general approach to the nonperturbative treatment of quantum field theories based on existence of effective gauge theory on auxiliary ''spectral" Riemann curve. We propose an effective formulation for the exact solutions to…

We prove that the topological recursion formalism can be used to quantize any generic classical spectral curve with smooth ramification points and simply ramified away from poles. For this purpose, we build both the associated quantum…

The geometric action on a certain orbit of the group of the area-preserving diffeomorphisms is considered, and it is shown, that it coincides with a special reduction of the three-dimensional Chern-Simons theory, under which group and space…

The observable properties of topological quantum matter are often described by topological field theories. We here demonstrate that this principle extends beyond thermal equilibrium. To this end, we construct a model of two-dimensional…

Description of two three-dimensional topological quantum field theories of Witten type as twisted supersymmetric theories is presented. Low-energy effective action and a corresponding topological invariant of three-dimensional manifolds are…

We compute the semiclassical formulas for the partition functions obtained using two different Lagrangians: the Chern-Simons functional and the symplectic action functional.

The paper contains the construction of a topological quantum field theory with corners that underlies the smooth topological quantum field theory of Lickorish. Among other things, a contraction formula for diagrams is proved, the presence…

In this work the generation of generalized Chern-Simons terms in three dimensional quantum electrodynamics with high spatial derivatives is studied. We analyze the self-energy corrections to the gauge field propagator by considering an…

The goal of this paper is to introduce some of the major ideas behind extended topological quantum field theories with an emphasis on explicit examples and calculations. The statement of the Cobordism Hypothesis is explained and immediately…

The functional integral computation of the various topological invariants, which are associated with the Chern-Simons field theory, is considered. The standard perturbative setting in quantum field theory is rewieved and new developments in…

We show that the four-dimensional Chern-Simons theory studied by Costello, Witten and Yamazaki, is, with Nahm pole-type boundary conditions, dual to a boundary theory that is a three-dimensional analogue of Toda theory with a novel 3d…