SU(3) x SU(3) compactification and mirror duals of magnetic fluxes

TL;DR

This paper explores type II string theories on backgrounds with SU(3) x SU(3) structure, revealing mirror symmetry and dual couplings related to Calabi-Yau compactifications with magnetic fluxes, despite their non-geometric nature.

Contribution

It extends the analysis of SU(3) backgrounds to SU(3) x SU(3) structures, demonstrating mirror symmetry and dual flux couplings in a broader class of string backgrounds.

Findings

Mirror symmetric effective couplings are obtained.

Backgrounds are often non-geometric, challenging supergravity validity.

Naive geometric formulas still yield correct low-energy theories.

Abstract

This paper analyses type II string theories in backgrounds which admit an SU(3) x SU(3) structure. Such backgrounds are designed to linearly realize eight out of the original 32 supercharges and as a consequence the low-energy effective action can be written in terms of couplings which are closely related to the couplings of four-dimensional N=2 theories. This generalizes the previously studied case of SU(3) backgrounds in that the left- and right-moving sector each have a different globally defined spinor. Given a truncation to a finite number of modes, these backgrounds lead to a conventional four-dimensional low-energy effective theory. The results are manifestly mirror symmetric and give terms corresponding to the mirror dual couplings of Calabi-Yau compactifications with magnetic fluxes. It is argued, however, that generically such backgrounds are non-geometric and hence the supergravity analysis is not strictly valid. Remarkably, the naive generalization of the geometrical expressions nonetheless appears to give the correct low-energy effective theory.