New topological field theories in two dimensions

TL;DR

This paper introduces a new class of two-dimensional topological field theories derived from free Abelian and non-Abelian gauge theories, combining features of Witten and Schwarz types and providing tractable models for Hodge theory.

Contribution

It identifies and characterizes a novel class of 2D topological field theories that unify features of Witten and Schwarz types, with explicit topological invariants and recursion relations.

Findings

Theories capture key features of both Witten and Schwarz topological theories.

Topological invariants are computed on 2D compact manifolds.

Theories serve as tractable models for 2D Hodge theory.

Abstract

It is shown that two$(1 + 1)$-dimensional (2D) free Abelian- and self-interacting non-Abelian gauge theories (without any interaction with matter fields) belong to a new class of topological field theories. These new theories capture together some of the key features of Witten- and Schwarz type of topological field theories because they are endowed with symmetries that are reminiscent of the Schwarz type theories but their Lagrangian density has the appearance of the Witten type theories. The topological invariants for these theories are computed on a 2D compact manifold and their recursion relations are obtained. These new theories are shown to provide a class of tractable field theoretical models for the Hodge theory in two dimensions of flat (Minkowski) spacetime where there are no propagating degrees of freedom associated with the 2D gauge boson.