Topological current algebras in two dimensions

TL;DR

This paper constructs two-dimensional topological field theories with non-abelian current symmetry, analyzing their conformal algebra which differs from twisted N=2 models, and interprets them as topological sigma models for group manifolds.

Contribution

It introduces a new class of topological field theories with non-abelian currents and analyzes their unique conformal algebra structure.

Findings

The models possess a linear algebra of generators with dimensions 1, 2, and 3.

The topological conformal algebra differs from twisted N=2 superconformal models.

The theories can be interpreted as topological sigma models for group manifolds.

Abstract

Two-dimensional topological field theories possessing a non-abelian current symmetry are constructed. The topological conformal algebra of these models is analysed. It differs from the one obtained by twisting the $N=2$ superconformal models and contains generators of dimensions $1$, $2$ and $3$ that close a linear algebra. Our construction can be carried out with one and two bosonic currents and the resulting theories can be interpreted as topological sigma models for group manifolds