4-D gauged supergravity analysis of Type IIB vacua on K3×T2/Z2K3\times T^2/Z_2K3×T2/Z2 (original) (raw)
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4-D gauged supergravity analysis of Type IIB vacua on K3 × T2/Z2
2000
We analyze N = 2,1,0 vacua of type IIB string theory on K3 × T2/Z2 in presence of three-form fluxes from a four dimensional su- pergravity viewpoint. The quaternionic geometry of the K3 moduli space together with the special geometry of the NS and R-R dila- tons and of the T2-complex structure moduli play a crucial role in the analysis.
4-D gauged supergravity analysis of type-IIB vacua on K3× T2/Bbb Z2
We analyze N = 2, 1, 0 vacua of type IIB string theory on K3 × T 2 /Z 2 in presence of three-form fluxes from a four dimensional supergravity viewpoint. The quaternionic geometry of the K3 moduli space together with the special geometry of the NS and R-R dilatons and of the T 2 -complex structure moduli play a crucial role in the analysis. The introduction of fluxes corresponds to a particular gauging of N = 2, D = 4 supergravity. Our results agree with a recent work of Tripathy and Trivedi. The present formulation shows the power of supergravity in the study of effective theories with broken supersymmetry.
4-D gauged supergravity analysis of type IIB vacua on K3xT2/Z2
2003
We analyze N = 2, 1, 0 vacua of type IIB string theory on K3 × T 2 /Z 2 in presence of three-form fluxes from a four dimensional supergravity viewpoint. The quaternionic geometry of the K3 moduli space together with the special geometry of the NS and R-R dilatons and of the T 2-complex structure moduli play a crucial role in the analysis. The introduction of fluxes corresponds to a particular gauging of N = 2, D = 4 supergravity. Our results agree with a recent work of Tripathy and Trivedi. The present formulation shows the power of supergravity in the study of effective theories with broken supersymmetry.
Type IIB flux vacua from G-theory I
Journal of High Energy Physics, 2015
We construct non-perturbatively exact four-dimensional Minkowski vacua of type IIB string theory with non-trivial fluxes. These solutions are found by gluing together, consistently with U-duality, local solutions of type IIB supergravity on T 4 ×C with the metric, dilaton and flux potentials varying along C and the flux potentials oriented along T 4. We focus on solutions locally related via U-duality to non-compact Ricci-flat geometries. More general solutions and a complete analysis of the supersymmetry equations are presented in the companion paper [1]. We build a precise dictionary between fluxes in the global solutions and the geometry of an auxiliary K3 surface fibered over CP 1. In the spirit of F-theory, the flux potentials are expressed in terms of locally holomorphic functions that parametrize the complex structure moduli space of the K3 fiber in the auxiliary geometry. The brane content is inferred from the monodromy data around the degeneration points of the fiber.
Journal of High Energy Physics, 2003
We derive the lagrangian and the transformation laws of N = 4 gauged supergravity coupled to matter multiplets whose σ-model of the scalars is SU(1, 1)/U(1) ⊗ SO(6, 6 + n)/SO(6) ⊗ SO(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 ⊗ 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. Contents 1. Introduction 1 2. The geometry of the scalar sector of the T 6 /Z 2 orientifold in presence of D3-branes 4 2.1 The σ-model of the bulk supergravity sector 4 2.2 Geometry of the σ-model in presence of n D3-branes 9 3. The symplectic embedding and duality rotations 11 4. The gauging 13 5. Space-time lagrangian 16 6. The scalar potential and its extrema 19 7. The mass spectrum 22 8. Embedding of the N = 4 model with six matter multiplets in the N = 8 24 8.1 The masses in the N = 4 theory with gauged Peccei-Quinn isometries and USp(8) weights 28 8.2 Duality with a truncation of the spontaneously broken N = 8 theory from Scherk-Schwarz reduction 30 A. The solution of the Bianchi identities and the supersymmetry transformation laws 34 B. Derivation of the space time lagrangian from the geometric approach 39 C. The moduli of T 6 in real and complex coordinates 42 D. Conventions 45 42 −→ 20 0 + 1 +2 + 1 −2 + 10 +1 + 10 −1 (1.5) and the vacuum condition of the N = 4 orientifold theory corresponds to setting to zero [50, 57] the representation 10 −1 (the other representations being deleted in the truncation).
Type IIB flux vacua from G-theory II
Journal of High Energy Physics, 2015
We find analytic solutions of type IIB supergravity on geometries that locally take the form Mink×M 4 ×C with M 4 a generalised complex manifold. The solutions involve the metric, the dilaton, NSNS and RR flux potentials (oriented along the M 4) parametrised by functions varying only over C. Under this assumption, the supersymmetry equations are solved using the formalism of pure spinors in terms of a finite number of holomorphic functions. Alternatively, the solutions can be viewed as vacua of maximally supersymmetric supergravity in six dimensions with a set of scalar fields varying holomorphically over C. For a class of solutions characterised by up to five holomorphic functions, we outline how the local solutions can be completed to four-dimensional flux vacua of type IIB theory. A detailed study of this global completion for solutions with two holomorphic functions has been carried out in the companion paper [1]. The fluxes of the global solutions are, as in F-theory, entirely codified in the geometry of an auxiliary K3 fibration over CP 1. The results provide a geometric construction of fluxes in F-theory.
D = 4, N = 2 Gauged Supergravity
2003
Using superspace techniques we construct the general theory describing D = 4, N = 2 supergravity coupled to an arbitrary number of vector and scalar–tensor multiplets. The scalar manifold of the theory is the direct product of a special Kähler and a reduction of a Quaternionic–Kähler manifold. We perform the electric gauging of a subgroup of the isometries of such manifold as well as " magnetic " deformations of the theory discussing the consistency conditions arising in this process. The resulting scalar potential is the sum of a symplectic invariant part (which in some instances can be recast into the standard form of the gauged N = 2 theory) and of a non–invariant part, both giving new deformations. We also show the relation of such theories to flux compactifications of type II string theories.
Twelve-Dimensional Aspects of Four-Dimensional N= 1 Type I Vacua
Phys.Lett. B387 (1996) 64-70, 1996
Four-dimensional supergravity theories are reinterpreted in a 12-dimensional Ftheory framework. The O(8) symmetry of N = 8 supergravity is related to a reduction of F-theory on T 8 , with the seventy scalars formally associated, by O(8) triality, to a fully compactified four-form A 4 . For the N = 1 type I model recently obtained from the type IIB string on the Z orbifold, we identify the Kähler manifold of the untwisted scalars in the unoriented closed sector with the generalized Siegel upper-half plane Sp(8, R)/(SU (4) × U (1)). The SU (4) factor reflects the holonomy group of Calabi-Yau fourfolds.
D=4, gauged supergravity in the presence of tensor multiplets
Nuclear Physics B, 2004
Using superspace techniques we construct the general theory describing D = 4, N = 2 supergravity coupled to an arbitrary number of vector and scalar-tensor multiplets. The scalar manifold of the theory is the direct product of a special Kähler and a reduction of a Quaternionic-Kähler manifold. We perform the electric gauging of a subgroup of the isometries of such manifold as well as "magnetic" deformations of the theory discussing the consistency conditions arising in this process. The resulting scalar potential is the sum of a symplectic invariant part (which in some instances can be recast into the standard form of the gauged N = 2 theory) and of a non-invariant part, both giving new deformations. We also show the relation of such theories to flux compactifications of type II string theories.
On Type IIB moduli stabilization and supergravities
Nuclear Physics B, 2011
We analyze D = 4 compactifications of Type IIB theory with generic, geometric and non-geometric, dual fluxes turned on. In particular, we study N = 1 toroidal orbifold compactifications that admit an embedding of the untwisted sector into gauged N = 4, 8 supergravities. Truncations, spontaneous breaking of supersymmetry and the inclusion of sources are discussed. The algebraic identities satisfied by the supergravity gaugings are used to implement the full set of consistency constraints on the background fluxes. This allows to perform a generic study of N = 1 vacua and identify large regions of the parameter space that do not admit complete moduli stabilization. Illustrative examples of AdS and Minkowski vacua are presented.