String Theory on G_2 Manifolds Based on Gepner Construction

TL;DR

This paper constructs modular invariant partition functions for string theories on G_2 manifolds using Gepner models, revealing new massless states in twisted sectors when certain levels are even.

Contribution

It introduces a method to build G_2 manifold models from Gepner models and analyzes the resulting massless spectra, including new states in specific cases.

Findings

Constructed modular invariant partition functions for G_2 manifolds.

Identified the presence of tricritical Ising models in conformal blocks.

Discovered extra massless states in twisted sectors for even levels.

Abstract

We study the type II string theories compactified on manifolds of $G_2$ holonomy of the type $({Calabi-Yau 3-fold} \times S^1)/\bz_2$ where $CY_3$ sectors realized by the Gepner models. We construct modular invariant partition functions for $G_2$ manifold for arbitrary Gepner models of the Calabi-Yau sector. We note that the conformal blocks contain the tricritical Ising model and find extra massless states in the twisted sectors of the theory when all the levels $k_i$ of minimal models in Gepner constructions are even.