CFT Description of String Theory Compactified on Non-compact Manifolds with G_2 Holonomy

TL;DR

This paper constructs modular invariant partition functions for string theory on non-compact G_2 holonomy manifolds, revealing a connection to tricritical Ising models and extending to Spin(7) cases.

Contribution

It introduces a novel construction of partition functions involving minimal models for non-compact G_2 manifolds, linking to tricritical Ising models and generalizing previous results.

Findings

Partition functions exhibit G_2 holonomy features

Amplitudes relate to tricritical Ising models

Candidate partition function for Spin(7) manifolds

Abstract

We construct modular invariant partition functions for strings propagating on non-compact manifolds of G_2 holonomy. Our amplitudes involve a pair of N=1 minimal models M_m, M_{m+2} (m=3,4,...) and are identified as describing strings on manifolds of G_2 holonomy associated with A_{m-2} type singularity. It turns out that due to theta function identities our amplitudes may be cast into a form which contain tricritical Ising model for any m. This is in accord with the results of Shatashvili and Vafa. We also construct a candidate partition function for string compactified on a non-compact Spin(7) manifold.