Low energy models of string theory

TL;DR

This paper reviews various string theory compactification methods, emphasizing Calabi-Yau manifolds and flux compactifications, and explores applications in cosmology and non-relativistic string theories, highlighting open research questions.

Contribution

It provides a comprehensive overview of string compactification schemes, including flux and non-relativistic theories, and discusses their implications in cosmology and open problems.

Findings

Calabi-Yau manifolds are necessary for fluxless compactifications.

Flux compactifications utilize generalized complex geometry.

Applications include cosmological models and non-relativistic string theories.

Abstract

String theory is the prime candidate for the theory of everything. However, it must be defined in ten dimensions to be consistent. To get 4D physics, the 6 other dimensions should be curled up in a small compact manifold, this procedure is called string compactification. In this review, we will review different compactification schemes proving that in absence of flux, the compact manifold must be a Calabi-Yau manifold. Then, we review compactifications with flux using generalized complex geometry. We then discuss some applications in cosmology like the swampland project and the cosmological models derived from it. We then discuss non relativistic string theories and introduce a toroidal compactifications for such theories. Finally, we discuss some open questions in the field.