Landau-Ginzburg Vacua of String, M- and F-Theory at c=12

TL;DR

This paper explores Landau-Ginzburg and geometric phases of certain Calabi-Yau fourfold models in string theory, analyzing their properties, moduli space connectivity, and mirror symmetry across over a million configurations.

Contribution

It provides a detailed analysis of Calabi-Yau fourfolds with both Landau-Ginzburg and geometric phases, including a large classification of configurations and their mirror symmetry properties.

Findings

Analyzed cohomology and moduli space connectivity.

Constructed and classified over 1 million configurations.

Identified mirror symmetry relations among models.

Abstract

Theories in more than ten dimensions play an important role in understanding nonperturbative aspects of string theory. Consistent compactifications of such theories can be constructed via Calabi-Yau fourfolds. These models can be analyzed particularly efficiently in the Landau-Ginzburg phase of the linear sigma model, when available. In the present paper we focus on those sigma models which have both a Landau-Ginzburg phase and a geometric phase described by hypersurfaces in weighted projective five-space. We describe some of the pertinent properties of these models, such as the cohomology, the connectivity of the resulting moduli space, and mirror symmetry among the 1,100,055 configurations which we have constructed.