Superconformal Field Theories for Compact G_2 Manifolds

TL;DR

This paper constructs exactly solvable superconformal field theories for Type II string compactifications on G_2 manifolds, revealing discrepancies with supergravity predictions due to discrete flux backgrounds.

Contribution

It introduces a new class of superconformal models for G_2 compactifications using Gepner models and analyzes their spectra, highlighting flux effects.

Findings

Massless spectra differ from supergravity expectations.

Discrete NS-NS flux explains spectral discrepancies.

Models are based on anti-holomorphic quotients of CY*S^1

Abstract

We present the construction of exactly solvable superconformal field theories describing Type II string models compactified on compact G_2 manifolds. These models are defined by anti-holomorphic quotients of the form (CY*S^1)/Z_2, where we realize the Calabi-Yau as a Gepner model. In the superconformal field theory the Z_2 acts as charge conjugation implying that the representation theory of a W(2,4,6,8,10) algebra plays an important role in the construction of these models. Intriguingly, in all three examples we study, including the quintic, the massless spectrum in the Z_2 twisted sector of the superconformal field theory differs from what one expects from the supergravity computation. This discrepancy is explained by the presence of a discrete NS-NS background two-form flux in the Gepner model.