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

Riccardo D'Auria, Sergio Ferrara, Floriana Gargiulo, Mario Trigiante, Silvia Vaula

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.

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

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.

Paper Structure

This paper contains 12 sections, 205 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. The Geometry of the scalar sector of the $T^6/\mathbb{Z}_2$ orientifold in presence of $D3$--branes
  3. The $\sigma$--model of the bulk supergravity sector
  4. Geometry of the $\sigma$--model in presence of $n$ $D3$--branes
  5. The symplectic embedding and duality rotations
  6. The Gauging
  7. Space--time Lagrangian
  8. The scalar potential and its extrema
  9. The mass spectrum
  10. Embedding of the $N=4$ model with six matter multiplets in the $N=8$
  11. The masses in the $N=4$ theory with gauged Peccei--Quinn isometries and ${\rm USp}(8)$ weights
  12. Duality with a truncation of the spontaneously broken $N=8$ theory from Scherk--Schwarz reduction

Figures (2)

  • Figure 1: ${\rm E}_{7(7)}$ Dynkin diagram. The empty circles denote ${\rm SO}(6,6)_T$ roots, while the filled circle denotes the ${\rm SO}(6,6)_T$ spinorial weight.
  • Figure 2: ${\rm SL}(2,\mathbb{R})\times {\rm SO}(6,6)_T$ and ${\rm SL}(2,\mathbb{R})\times {\rm SO}(6,6)$ Dynkin diagrams. The root $\alpha$ is the ${\rm E}_{7(7)}$ highest root while $\beta$ is $\alpha_3+2\alpha_4+\alpha_5+2\alpha_6+\alpha_7$. The group ${\rm SL}(2,\mathbb{R})_{IIB}$ is the symmetry group of the ten dimensional type IIB theory.