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

TL;DR

The paper extends Landau–Ginzburg analyses to Calabi–Yau fourfolds at $c=12$, examining sigma-models with both a Landau–Ginzburg phase and a geometric phase realized as hypersurfaces in weighted projective five-space. By computing cohomology via LG methods, studying moduli-space connectivity through phase transitions, and exploring mirror symmetry (including fractional transformations), the authors assemble a vast dataset of $1{,}100{,}055$ LG theories and $667{,}954$ distinct spectra, revealing rich structure such as extensive mirror networks and complex fibration patterns. They demonstrate that the moduli space of these vacua is highly connected yet may be non-simply connected due to loop transitions, and they elucidate transversality and finiteness constraints that govern viable LG potentials. The results have implications for F-theory, M-theory, and heterotic dualities, offering a comprehensive map of fourfold vacua and their geometric and physical interrelations, including a detailed account of fibrations and their Hodge-number signatures.

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.