Topological Chern-Simons Sigma Model

TL;DR

This paper explores topological twists of three-dimensional Chern-Simons-matter theories with extended supersymmetry, constructing new models and revealing connections to topological invariants like Casson invariant.

Contribution

It classifies inequivalent topological twistings for N=4,5,6,8 supersymmetric theories and introduces a novel B-model based on complex Chern-Simons theory.

Findings

Constructed two N=4 topological models, A and B.

Identified the B-model as a complex Chern-Simons theory.

Connected the A-model to Casson invariant and Rozansky-Witten theory.

Abstract

We consider topological twisting of recently constructed Chern-Simons-matter theories in three dimensions with N=4 or higher supersymmetry. We enumerate physically inequivalent twistings for each N, and find two different twistings for N=4, one for N=5,6, and four for N=8. We construct the two types of N=4 topological theories, which we call A/B-models, in full detail. The A-model has been recently studied by Kapustin and Saulina. The B-model is new and it consists solely of a Chern-Simons term of a complex gauge field up to BRST-exact terms. We also compare the new theories with topological Yang-Mills theories and find some interesting connections. In particular, the A-model seems to offer a new perspective on Casson invariant and its relation to Rozansky-Witten theory.