Unusual gauged supergravities from type IIA and type IIB orientifolds

TL;DR

This work classifies unusual gauged ${\nc{N}=4}$ supergravities arising from type II orientifolds with fluxes, showing that turning on NS-NS and R-R fluxes generates non-semisimple gauge algebras embedded in ${\rm so}(6,6)$ with central extensions and non-metric axions acquiring Stueckelberg couplings. It analyzes IIB orientifolds with fluxes (p=7,5) and IIA orientifolds (p=8,6,4), detailing how fluxes produce non-abelian gaugings and how the gauge algebra is realized both directly and in terms of isometries of the scalar manifold, subject to algebra-closure constraints like $H^{\ā}_{ij}H^{ij}_{\ā}=0$ or $V^c = \epsilon^{ijk}\epsilon^{abc} F_{ia} H_{jkb} = 0$. The results reveal a non-commutative torus structure when $H$-flux is present and show central extensions of solvable algebras generated by Peccei-Quinn symmetries, providing a cohesive picture of how fluxes shape the vacua and low-energy dynamics of ${\nc{N}=4}$ theories from orientifold compactifications.

Abstract

We analyse different N=4 supergravities coupled to six vector multiplets corresponding to low-energy descriptions of the bulk sector of T6/Z2 orientifolds with p-brane in IIB (p odd) and in IIA (p even) superstrings. When fluxes are turned on, a gauging emerges corresponding to some non-semisimple Lie algebra related to nilpotent algebras N_p inside so(6,6), with dimension 15 + (p-3)(9-p). The non-metric axions have Stueckelberg couplings that induce a spontaneous breaking of gauge symmetries. In four cases the gauge algebra is non-abelian with a non-commutative structure of the compactification torus, due to fluxes of NS-NS and R-R forms.