Open G2 Strings

TL;DR

This paper explores the open string topological twist on G2 manifolds, relating string states to geometric deformations and gauge theories, and connects these to known models in special cases.

Contribution

It introduces a detailed analysis of open string states on G2 manifolds and relates them to geometric and gauge-theoretic structures, extending known theories.

Findings

Open strings on G2 manifolds relate to deformations of calibrated submanifolds.

Associative cycles correspond to a gauge-fixed Chern-Simons theory.

Reduction to Calabi-Yau times circle yields open A-model and B-model results.

Abstract

We consider an open string version of the topological twist previously proposed for sigma-models with G2 target spaces. We determine the cohomology of open strings states and relate these to geometric deformations of calibrated submanifolds and to flat or anti-self-dual connections on such submanifolds. On associative three-cycles we show that the worldvolume theory is a gauge-fixed Chern-Simons theory coupled to normal deformations of the cycle. For coassociative four-cycles we find a functional that extremizes on anti-self-dual gauge fields. A brane wrapping the whole G2 induces a seven-dimensional associative Chern-Simons theory on the manifold. This theory has already been proposed by Donaldson and Thomas as the higher-dimensional generalization of real Chern-Simons theory. When the G2 manifold has the structure of a Calabi-Yau times a circle, these theories reduce to a combination of the open A-model on special Lagrangians and the open B+\bar{B}-model on holomorphic submanifolds. We also comment on possible applications of our results.