SUSY SUGRA GEOMETRY · Supersymmetry, supergravity and geometry in particle physics and string theory

The Standard Model of particle physics, which has so far provided a successful description of elementary particles, is believed to be an incomplete theory. New experiments are starting to probe physics beyond the Standard Model. Supersymmetry, supergravity, and string theory are the theoretical tools that are expected to describe the new physics proposing solutions to fundamental problems such as the nature of dark matter, the unification of forces and the formulation of quantum gravity. Moreover, a symbiotic relation between string theory and mathematics has proven to be central for both fields. The present project aims at a deeper understanding of challenging features of supersymmetry, supergravity and string theories in the intersection of physics and mathematics. The applicant has recently developed a projective superspace approach to off-shell matter-coupled supergravity with eight supercharges in four- and five-dimensions. The main line of research we are proposing will focus on the application and extension of this approach. As a major application we will construct new quaternionic-Kahler geometries. The new techniques will be used to achieve a better understanding of 4D effective-actions in compactified string theory. Superspace approaches to supergravity theories are also relevant in studying extra-dimensional phenomenological scenarios in dimensions less than six. A second goal of the project concerns the study of 2D supersymmetric sigma-models having generalized complex manifolds as target spaces. Generalized complex geometry naturally arises in string theory and a better knowledge of the underlying mathematics will lead to powerful tools for the physicists. Using superspace techniques we will study the topological sectors of these theories that could give new insights on mirror symmetry, T-duality and related topics in the case of generalized-Kahler manifolds. Most importantly, applications to string compactifications with fluxes will be analyzed.