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New D=4 gauged supergravities from N=4 orientifolds with fluxes

C. Angelantonj, S. Ferrara, M. Trigiante

TL;DR

The paper analyzes four-dimensional ${ Scr N}=4$ orientifolds with fluxes, showing that different $T_6$ orientifold projections yield distinct duality embeddings and massless spectra. It identifies nilpotent axion algebras $N_p subseteq so(6,6)$ arising from RR and NS-NS axions, which determine the possible gaugings when fluxes are introduced. By embedding these theories into the ${ Scr N}=8$ framework with ${E}_{7(7)}$ duality, the authors derive the structure of the vector sector, scalar manifold, and the gauging mechanism via local Peccei–Quinn symmetries. The results provide a systematic route to generate new $D=4$ gauged ${ Scr N}=4$ supergravities with six bulk vector multiplets and a brane Yang–Mills sector, with implications for moduli stabilization and future extensions to ${ Scr N}=2,1$ models.

Abstract

We consider classes of T_6 orientifolds, where the orientifold projection contains an inversion I_{9-p} on 9-p coordinates, transverse to a Dp-brane. In absence of fluxes, the massless sector of these models corresponds to diverse forms of N=4 supergravity, with six bulk vector multiplets coupled to N=4 Yang--Mills theory on the branes. They all differ in the choice of the duality symmetry corresponding to different embeddings of SU(1,1)\times SO(6,6+n) in Sp(24+2n,R), the latter being the full group of duality rotations. Hence, these Lagrangians are not related by local field redefinitions. When fluxes are turned on one can construct new gaugings of N=4 supergravity, where the twelve bulk vectors gauge some nilpotent algebra which, in turn, depends on the choice of fluxes.

New D=4 gauged supergravities from N=4 orientifolds with fluxes

TL;DR

The paper analyzes four-dimensional orientifolds with fluxes, showing that different orientifold projections yield distinct duality embeddings and massless spectra. It identifies nilpotent axion algebras arising from RR and NS-NS axions, which determine the possible gaugings when fluxes are introduced. By embedding these theories into the framework with duality, the authors derive the structure of the vector sector, scalar manifold, and the gauging mechanism via local Peccei–Quinn symmetries. The results provide a systematic route to generate new gauged supergravities with six bulk vector multiplets and a brane Yang–Mills sector, with implications for moduli stabilization and future extensions to models.

Abstract

We consider classes of T_6 orientifolds, where the orientifold projection contains an inversion I_{9-p} on 9-p coordinates, transverse to a Dp-brane. In absence of fluxes, the massless sector of these models corresponds to diverse forms of N=4 supergravity, with six bulk vector multiplets coupled to N=4 Yang--Mills theory on the branes. They all differ in the choice of the duality symmetry corresponding to different embeddings of SU(1,1)\times SO(6,6+n) in Sp(24+2n,R), the latter being the full group of duality rotations. Hence, these Lagrangians are not related by local field redefinitions. When fluxes are turned on one can construct new gaugings of N=4 supergravity, where the twelve bulk vectors gauge some nilpotent algebra which, in turn, depends on the choice of fluxes.

Paper Structure

This paper contains 20 sections, 159 equations, 1 figure, 18 tables.

Table of Contents

  1. Introduction
  2. ${\Scr N}=4$ orientifolds: spectra and fluxes
  3. IIB orientifolds
  4. IIA orientifolds
  5. ${\Scr N}=4$ supergravity interpretation of $T_6$ orientifolds: manifest duality transformations and Peccei--Quinn symmetries.
  6. $T_4\times T_2$ IIB orientifold with D7 branes. The ungauged version.
  7. $T_2 \times T_4$ IIB orientifold with D5 branes. The ungauged version
  8. $T_0\times T_6$ and $T_6\times T_0$ IIB orientifolds with D3 and D9 branes. The ungauged version.
  9. $T_1\times T_5$ IIA orientifold with $D4$--branes.
  10. $T_3\times T_3$ IIA orientifold with $D6$--branes.
  11. $T_5\times T_1$ IIA orientifold with $D8$--branes
  12. Fluxes and gauged supergravity: local Peccei--Quinn symmetry as gauged duality transformations.
  13. The $T_4\times T_2$ IIB orientifold model
  14. Type $T_2\times T_4$ IIB orientifold model.
  15. Conclusions and outlooks
  16. ...and 5 more sections

Figures (1)

  • Figure 1: $SO(6,6)$ Dynkin diagrams for the $T_{p-3}\times T_{9-p}$ models. The shaded subdiagrams define the groups $SL(p-3, \mathbb{R})\times SL(9-p,\mathbb{R})$ acting transitively on the metric moduli. The empty circles define simple roots corresponding to the metric moduli $g_{ij},\,g_{ab}$, the grey circle denotes a simple root corresponding to a Kalb--Ramond field $B_{ia}$ and the black circle corresponds to a R--R axion.