Topological G$_{2}$ and Spin(7) strings at 1-loop from double complexes

TL;DR

This paper investigates topological $G_2$ and $Spin(7)$ strings at 1-loop, introducing new double complexes in generalized geometry, and relates the partition function to analytic torsion, providing new insights and predictions.

Contribution

It defines novel double complexes for supersymmetric NSNS backgrounds and connects the 1-loop partition function to analytic torsion, offering new predictions for $Spin(7)$ strings.

Findings

Reproduces the $G_2$ string calculation at 1-loop

Provides a new prediction for the $Spin(7)$ string

Links the partition function to analytic torsion in target space

Abstract

We study the topological $G_2$ and $Spin(7)$ strings at 1-loop. We define new double complexes for supersymmetric NSNS backgrounds of string theory using generalised geometry. The 1-loop partition function then has a target-space interpretation as a particular alternating product of determinants of Laplacians, which we have dubbed the analytic torsion. In the case without flux where these backgrounds have special holonomy, we reproduce the worldsheet calculation of the $G_2$ string and give a new prediction for the $Spin(7)$ string. We also comment on connections with topological strings on Calabi-Yau and K3 backgrounds.