Towards A Topological G_2 String

TL;DR

This paper introduces a new topological string theory based on G_2 holonomy manifolds, defining the theory, computing genus-zero correlators, and proposing extensions to all genera, with implications for three-dimensional physics.

Contribution

It defines a novel topological theory on G_2 manifolds, including the topological twist, BRST operator, and genus-zero correlators, and conjectures an extension to all genera.

Findings

Correlation functions relate to Hitchin's topological action

Topological string theory extended to G_2 manifolds

Differences from four-dimensional cases in physical implications

Abstract

We define new topological theories related to sigma models whose target space is a 7 dimensional manifold of G_2 holonomy. We show how to define the topological twist and identify the BRST operator and the physical states. Correlation functions at genus zero are computed and related to Hitchin's topological action for three-forms. We conjecture that one can extend this definition to all genus and construct a seven-dimensional topological string theory. In contrast to the four-dimensional case, it does not seem to compute terms in the low-energy effective action in three dimensions.