An Orientifold with Fluxes and Branes via T-duality

TL;DR

This paper develops a systematic method to construct the effective bosonic Lagrangian for T-dualized type I string theory with fluxes and branes, analyzing solutions with warped geometries and moduli stabilization.

Contribution

It provides a detailed construction of the effective Lagrangian including fluxes and D-branes in T-dualized type I theory, and compares results with gauged supergravity.

Findings

Derived warped Minkowski solutions with Ricci-flat internal manifolds.

Showed moduli stabilization via combined fluxes and gauge fields.

Confirmed consistency with N=4 gauged supergravity.

Abstract

String compactifications with non-abelian gauge fields localized on D-branes, with background NSNS and RR 3-form fluxes, and with non-trivial warp factors, can naturally exist within T-dual versions of type I string theory. We develop a systematic procedure to construct the effective bosonic Lagrangian of type I T-dualized along a six-torus, including the coupling to gauge multiplets on D3-branes and the modifications due to 3-form fluxes. Looking for solutions to the ten-dimensional equations of motion, we find warped products of Minkowski space and Ricci-flat internal manifolds. Once the warp factor is neglected, the resulting no-scale scalar potential of the effective four-dimensional theory combines those known for 3-form fluxes and for internal Yang-Mills fields and stabilizes many of the moduli. We perform an explicit comparison of our expressions to those obtained from N=4 gauged supergravity and find agreement. We also comment on the possibility to include D9-branes with world-volume gauge fluxes in the background with 3-form fluxes.