$P$ fluxes and exotic branes

TL;DR

This paper explores the role of P fluxes in type-II orientifold models, deriving superpotentials, flux transformation rules, and identifying exotic branes needed for consistency under T-duality.

Contribution

It provides a complete expression for the superpotential involving P fluxes and establishes transformation rules and constraints for fluxes and branes under T-duality.

Findings

Derived superpotential expressions for IIA and IIB theories.

Established T-duality transformation rules for P fluxes.

Identified exotic branes to cancel flux-induced tadpoles.

Abstract

We consider the ${\cal N}=1$ superpotential generated in type-II orientifold models by non-geometric fluxes. In particular, we focus on the family of $P$ fluxes, that are related by T-duality transformations to the S-dual of the $Q$ flux. We determine the general rule that transforms a given flux in this family under a single T-duality transformation. This rule allows to derive a complete expression for the superpotential for both the IIA and the IIB theory for the particular case of a $T^6/[\mathbb{Z}_2 \times \mathbb{Z}_2 ]$ orientifold. We then consider how these fluxes modify the generalised Bianchi identities. In particular, we derive a fully consistent set of quadratic constraints coming from the NS-NS Bianchi identities. On the other hand, the $P$ flux Bianchi identities induce tadpoles, and we determine a set of exotic branes that can be consistently included in order to cancel them. This is achieved by determining a universal transformation rule under T-duality satisfied by all the branes in string theory.