On the Topology of the Inflaton Field in Minimal Supergravity Models

We consider global issues in minimal supergravity models where a single field inflaton potential emerges. In a particular case we reproduce the Starobinsky model and its description dual to a certain formulation of R+R^2 supergravity. For definiteness we confine our analysis to spaces at constant curvature, either vanishing or negative. Five distinct models arise, two flat models with respectively a quadratic and a quartic potential and three based on the SU(1,1)/U(1) space where its distinct isometries, elliptic, hyperbolic and parabolic are gauged. Fayet-Iliopoulos terms are introduced in a geometric way and they turn out to be a crucial ingredient in order to describe the de Sitter inflationary phase of the Starobinsky model.Comment: 31 pages, LaTex, 7 eps figures, 2 table

R-Symmetry and the Topological Twist of N=2 Effective Supergravities of Heterotic Strings

We discuss R-symmetries in locally supersymmetric N=2 gauge theories coupled to hypermultiplets which can be thought of as effective theories of heterotic superstring models. In this type of supergravities a suitable R-symmetry exists and can be used to topologically twist the theory: the vector multiplet containing the dilaton-axion field has different R-charge assignments with respect to the other vector multiplets. Correspondingly a system of coupled instanton equations emerges, mixing gravitational and Yang--Mills instantons with triholomorphic hyperinstantons and axion-instantons. For the tree-level classical special manifolds $ST(n)=SU(1,1)/U(1)\times SO(2,n)/(SO(2)$ $\times SO(n))$ R-symmetry with the specified properties is a continuous symmetry, but for the quantum corrected manifolds ${\hat {ST}}(n)$ a discrete R--group of electric--magnetic duality rotations is sufficient and we argue that it exists.Comment: 40 pages, plain LaTeX. Final version to appear on IJMP

Hyperbolic Kac Moody Algebras and Einstein Billiards

We identify the hyperbolic Kac Moody algebras for which there exists a Lagrangian of gravity, dilatons and $p$-forms which produces a billiard that can be identified with their fundamental Weyl chamber. Because of the invariance of the billiard upon toroidal dimensional reduction, the list of admissible algebras is determined by the existence of a Lagrangian in three space-time dimensions, where a systematic analysis can be carried out since only zero-forms are involved. We provide all highest dimensional parent Lagrangians with their full spectrum of $p$-forms and dilaton couplings. We confirm, in particular, that for the rank 10 hyperbolic algebra, $CE_{10} = A_{15}^{(2)\wedge}$, also known as the dual of $B_8^{\wedge\wedge}$, the maximally oxidized Lagrangian is 9 dimensional and involves besides gravity, 2 dilatons, a 2-form, a 1-form and a 0-form.Comment: 33 page

Supersymmetric completion of M-theory 4D-gauge algebra from twisted tori and fluxes

We present the supersymmetric completion of the M-theory free differential algebra resulting from a compactification to four dimensions on a twisted seven-torus with 4-form and 7-form fluxes turned on. The super--curvatures are given and the local supersymmetry transformations derived. Dual formulations of the theory are discussed in connection with classes of gaugings corresponding to diverse choices of vacua. This also includes seven dimensional compactifications on more general spaces not described by group manifolds.Comment: 19 pages, LaTeX, typos corrected, references adde

Exploring Fermionic T-duality

The fermionic T-duality transformation developed by Berkovits and Maldacena is applied to D-brane and the pp-wave solutions of type IIB supergravity. The pp-wave is found to be self-dual under the combination of dualities. We explore the consequences of applying the transformation and discuss various properties of the new transformed solutions.Comment: 27 pages, latex, v2: refs adde

Two-Loop Renormalization Group Equations for Soft Supersymmetry-Breaking Couplings

We compute the two-loop renormalization group equations for all soft supersymmetry-breaking couplings in a general softly broken N=1 supersymmetric model. We also specialize these results to the Minimal Supersymmetric Standard Model.Comment: 26 pages. [v4: Signs of equations (4.2) and (4.3) are fixed.