Topological Chern-Simons/Matter Theories

TL;DR

This paper introduces a new topological 3D theory coupling Chern-Simons to matter, dependent only on transverse holomorphic foliation structures, with connections to string theory and potential condensed matter applications.

Contribution

It constructs a novel partially topological Chern-Simons/matter theory on 3-manifolds with THF, linking it to topological string theory and supersymmetric models.

Findings

The theory depends solely on the THF structure, not on the metric.

It is equivalent to an N=2 supersymmetric Chern-Simons matter theory.

Potential applications in condensed matter physics are discussed.

Abstract

We propose a new partially topological theory in three dimensions which couples Chern-Simons theory to matter. The 3-manifolds needed for this construction admit transverse holomorphic foliation (THF). The theory depends only on the choice of such a structure, but not on a choice of metric and in this sense, it is topological. We argue that this theory arises in topological A-model string theory on Lagrangian 3-branes in the presence of additional parallel coisotropic 5-branes. The theory obtained in this way is equivalent to an N=2 supersymmetric Chern-Simons matter theory on the same 3-manifold, which also only depends on the THF structure. The theory is a realization of a topological theory of class H, which allows splitting of a temporal direction from spatial directions. We briefly discuss potential condensed matter applications.