paper

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

arXiv:hep-th/0108091 · doi:10.1016/S0370-2693(01)01080-2

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.

It is found that tricritical Ising model is contained in our amplitues in agreement with the results of Shatashvili and Vafa. Manuscript is revised accordingly. A new reference is also added

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