Generalized Cohomologies and Supersymmetry

TL;DR

This paper links advanced mathematical cohomologies to string theory compactifications, introducing new generalized cohomologies that unify complex and symplectic cases for counting massless fields in supersymmetric models.

Contribution

It introduces a new set of generalized complex cohomologies that interpolate between known cohomologies, providing a unified framework for counting massless fields in string compactifications.

Findings

Complex and symplectic cohomologies relate to string flux compactifications.

New generalized cohomologies unify previous frameworks.

Application to counting scalar moduli in Minkowski compactifications.

Abstract

We show that the complex cohomologies of Bott, Chern, and Aeppli and the symplectic cohomologies of Tseng and Yau arise in the context of type II string theory. Specifically, they can be used to count a subset of scalar moduli fields in Minkowski compactification with RR fluxes in the presence of either O5/D5 or O6/D6 brane sources, respectively. Further, we introduce a new set of cohomologies within the generalized complex geometry framework which interpolate between these known complex and symplectic cohomologies. The generalized complex cohomologies play the analogous role for counting massless fields for a general supersymmetric Minkowski type II compactification with Ramond-Ramond flux.