Jan Louis

Type II theories compactified on Calabi–Yau threefolds in the presence of background fluxes

Compactifications of type II theories on Calabi-Yau threefolds including electric and magnetic background fluxes are discussed. We derive the bosonic part of the four-dimensional low energy effective action and show that it is a non-canonical N=2 supergravity which includes a massive two-form. The symplectic invariance of the theory is maintained as long as the flux parameters transform as a symplectic vector and a massive two-form which couples to both electric and magnetic field strengths is present. The mirror symmetry between type IIA and type IIB compactified on mirror manifolds is shown to hold for R-R fluxes at the level of the effective action. We also compactify type IIA in the presence of NS three-form flux but the mirror symmetry in this case remains unclear.

Hitchin functionals in N = 2 supergravity

We consider type II string theory in space-time backgrounds which admit eight supercharges. Such backgrounds are characterized by the existence of a (generically non-integrable) generalized SU(3) × SU(3) structure. We demonstrate how the corresponding ten-dimensional supergravity theories can in part be rewritten using generalised O(6,6)-covariant fields, in a form that strongly resembles that of four-dimensional N = 2 supergravity, and precisely coincides with such after an appropriate Kaluza-Klein reduction. Specifically we demonstrate that the NS sector admits a special Kahler geometry with Kahler potentials given by the Hitchin functionals. Furthermore we explicitly compute the N = 2 version of the superpotential from the transformation law of the gravitinos, and find its N = 1 counterpart.

The effective action of D7-branes in N=1 Calabi–Yau orientifolds

Abstract Using a Kaluza–Klein reduction of the Dirac–Born–Infeld and Chern–Simons action we compute the four-dimensional N = 1 effective action for the massless modes of a D7-brane which is wrapped on a four-cycle of a compact Calabi–Yau orientifold. We do not consider a specific orientifold but instead determine the Kahler potential, the gauge kinetic functions and the scalar potential in terms of geometrical data of a generic orientifold and its wrapped four-cycle. In particular we derive the couplings of the D-brane excitations to the bulk moduli of the orientifold as they are important for the study of soft supersymmetry breaking terms. We relate the resulting Kahler geometry to the N = 1 special geometry of Lerche, Mayr and Warner. Finally we comment on the structure of the D-term which is induced by a Green–Schwarz term in the Chern–Simons action.

M theory compactified on Calabi-Yau fourfolds with background flux

Abstract We perform the Kaluza–Klein reduction of M-theory on warped Calabi–Yau fourfolds with non-trivial four-form flux turned on. The resulting scalar- and superpotential is computed and compared with the superpotential obtained by Gukov, Vafa and Witten using different methods.

SU(3) × SU(3) compactification and mirror duals of magnetic fluxes

This paper analyses type II string theories in backgrounds which admit an SU(3) × SU(3) structure. Such backgrounds are designed to linearly realize eight out of the original 32 supercharges and as a consequence the low-energy effective action can be written in terms of couplings which are closely related to the couplings of four-dimensional N = 2 theories. This generalizes the previously studied case of SU(3) backgrounds in that the left- and right-moving sector each have a different globally defined spinor. Given a truncation to a finite number of modes, these backgrounds lead to a conventional four-dimensional low-energy effective theory. The results are manifestly mirror symmetric and give terms corresponding to the mirror dual couplings of Calabi-Yau compactifications with magnetic fluxes. It is argued, however, that generically such backgrounds are non-geometric and hence the supergravity analysis is not strictly valid. Remarkably, the naive generalization of the geometrical expressions nonetheless appears to give the correct low-energy effective theory.

D-terms and F-terms from D7-brane fluxes

Abstract Using a Kaluza–Klein reduction of the fermionic part of the D-brane action we compute D- and F-terms of the N = 1 effective action for generic Calabi–Yau orientifold compactifications in the presence of a space–time filling D7-brane. We include non-trivial background fluxes for the D7-brane U ( 1 ) field strength on the internal four-cycle wrapped by the brane. First the four-dimensional fermionic spectrum arising from the D7-brane is derived and then the D- and F-terms are obtained by computing appropriate couplings of these fermionic fields. For specific examples we examine the resulting flux-induced scalar potentials and comment on their relevance in string cosmology.

Constraints on modular inflation in supergravity and string theory

We perform a general algebraic analysis on the possibility of realising slow-roll inflation in the moduli sector of string models. This problem turns out to be very closely related to the characterisation of models admitting metastable vacua with non-negative cosmological constant. In fact, we show that the condition for the existence of viable inflationary trajectories is a deformation of the condition for the existence of metastable de Sitter vacua. This condition depends on the ratio between the scale of inflation and the gravitino mass and becomes stronger as this parameter grows. After performing a general study within arbitrary supergravity models, we analyse the implications of our results in several examples. More concretely, in the case of heterotic and orientifold string compactifications on a Calabi-Yau in the large volume limit we show that there may exist fully viable models, allowing both for inflation and stabilisation. Additionally, we show that subleading corrections breaking the no-scale property shared by these models always allow for slow-roll inflation but with an inflationary scale suppressed with respect to the gravitino scale. A scale of inflation larger than the gravitino scale can also be achieved under more restrictive circumstances and only for certain types of compactifications.

Building an explicit de Sitter

A bstractWe construct an explicit example of a de Sitter vacuum in type IIB string theory that realizes the proposal of Kähler uplifting. As the large volume limit in this method depends on the rank of the largest condensing gauge group we carry out a scan of gauge group ranks over the Kreuzer-Skarke set of toric Calabi-Yau threefolds. We find large numbers of models with the largest gauge group factor easily exceeding a rank of one hundred. We construct a global model with Kähler uplifting on a two-parameter model on

Non-perturbative properties of heterotic string vacua compactified on K3 × T2

\mathbb{CP}_{11169}^4

Heterotic string theory with background fluxes

, by an explicit analysis from both the type IIB and F-theory point of view. The explicitness of the construction lies in the realization of a D7 brane configuration, gauge flux and RR and NS flux choices, such that all known consistency conditions are met and the geometric moduli are stabilized in a metastable de Sitter vacuum with spontaneous GUT scale supersymmetry breaking driven by an F-term of the Kähler moduli.