N=4 Supergravity Lagrangian for Type IIB Orientifold on T^6/Z_2 in Presence of Fluxes and D3-Branes

TL;DR

This paper derives the N=4 supergravity Lagrangian for Type IIB string theory compactified on T^6/Z_2 with fluxes and D3-branes, revealing its structure, gauge group, and relation to Scherk-Schwarz reduction.

Contribution

It provides the explicit form of the N=4 gauged supergravity Lagrangian for this compactification, including matter couplings and gauge group details, extending previous models.

Findings

The gauge group is T^{12} x G, with G on the branes.

The bulk spectrum satisfies quadratic and quartic mass sum rules.

The theory exhibits a no-scale supergravity with partial super-Higgs.

Abstract

We derive the Lagrangian and the transformation laws of N=4 gauged supergravity coupled to matter multiplets whose sigma-model of the scalars is SU(1,1)/U(1)x SO(6,6+n)/SO(6)xSO(6+n) and which corresponds to the effective Lagrangian of the Type IIB string compactified on the T^6/Z_2 orientifold with fluxes turned on and in presence of n D3-branes. The gauge group is T^12 x G where G is the gauge group on the brane and T^12 is the gauge group on the bulk corresponding to the gauged translations of the R-R scalars coming from the R-R four--form. The N=4 bulk sector of this theory can be obtained as a truncation of the Scherk-Schwarz spontaneously broken N=8 supergravity. Consequently the full bulk spectrum satisfies quadratic and quartic mass sum rules, identical to those encountered in Scherk-Schwarz reduction gauging a flat group. This theory gives rise to a no scale supergravity extended with partial super-Higgs mechanism.