The Topological G2 String

TL;DR

This paper introduces a new topological string theory based on G_2 holonomy manifolds, defining a novel topological twist and exploring its properties, including correlation functions and connections to Hitchin's functional.

Contribution

It constructs a seven-dimensional topological string theory with a new twist, extending the framework of topological models to G_2 manifolds and relating it to known models in special cases.

Findings

Defined a new topological twist for G_2 manifolds

Computed genus zero correlation functions related to Hitchin's functional

Extended the model to all genera and connected to existing topological models

Abstract

We construct new topological theories related to sigma models whose target space is a seven dimensional manifold of G_2 holonomy. We define a new type of topological twist and identify the BRST operator and the physical states. Unlike the more familiar six dimensional case, our topological model is defined in terms of conformal blocks and not in terms of local operators of the original theory. We also present evidence that one can extend this definition to all genera and construct a seven-dimensional topological string theory. We compute genus zero correlation functions and relate these to Hitchin's functional for three-forms in seven dimensions. Along the way we develop the analogue of special geometry for G_2 manifolds. When the seven dimensional topological twist is applied to the product of a Calabi-Yau manifold and a circle, the result is an interesting combination of the six dimensional A- and B-models.