Flux geometries, gauge theories and strings

Ever since Einstein`s general relativity provided a description of gravitational forces in terms of a curved space- time the intuitive and universal concepts of geometry belong to the most beautiful and efficient building blocks of our understanding of fundamental interactions. This realm of ideas has found an interesting refinement and extension with the advent of string theory: Already in the semi-classical sector of the theory the hidden dimensions enable a geometrization of all interactions. But beyond classical geometry, T-dualities and their generalizations imply identifications between geometries with large hidden dimensions and small internal geometries (or non-geometrical generalizations thereof), in which quantum corrections play a crucial role. Such phenomena are often subsumed by the term "quantum geometry". An even more drastical extension of geometrical concepts follows from the consideration of non-perturbative dualities and degrees of freedom. In this context the central objects are D-branes, which are extended solitonic objects whose singularity structure determines the observable matter fields and their interactions. D-branes are also the source of RR-fluxes which can be thought of as generalized electromagnetic fields in higher dimensions. It turned out recently that these fields are indispensable ingredients of the construction of realistic string models. Their quantization conditions on compact spaces imply discrete values of effective couplings and thus are vital for the predictability of the theory. RR-fluxes are also essential ingredients of the AdS/CFT duality, which relates strongly coupled gauge theories to weakly coupled dual models. The description of the dual string theories beyond the supergravity approximation requires their quantization in the presence of non-trivial RR- backgrounds, which was enabled by Berkovits` pure spinor formulation. In the present project we want to combine the methods of generalized geometries with constructions of doubled geometries that arise in the context of T-dualities in order to extend their power and generality and in order to improve and generalize results in the context of AdS/CFT duality and other applications. Here the use of the Berkovits formalism enables the quantization of the string in the presence of RR-fluxes and thus the computation of genuine string corretions beyond the supergravity approximation. The use of doubled formalisms, on the other hand, shall enable consideration of non-geometrical backgrounds and the inclusion of larger classes of dualites. While the focus of the proposal is on applications in the context of string/gauge dualities we also want to consider implications of our findings for the topic of compactification in the presence of D-branes and fluxes.

Ever since Einstein succeeded in describing gravitational forces by curved spacetime in his theory of general relativity, the intuitive and universal concepts of geometry constitute one of the most beautiful as well as most efficient building blocks of our understanding of fundamental physics. String theory has brought about interesting generalizations and a deeper understanding of these ideas. Already in the semiclassical sector of string theory hidden dimensions allow for a geometrization of all known interactions. Beyond classical geometry, T dualities and their generalizations imply relations between models involving large hidden dimensions and those with small inner geometries (and also "non-geometrical" generalizations thereof), where quantum corrections play a decisive role, leading to the notion of "quantum geometry". Including nonperturbative features and dualities leads to even more drastic extensions of these geometric concepts, in which a central role is played by D branes - extended objects whose singularity structure determines physical matter and its properties. D branes are also sources for so-called RR fluxes, which can be viewed as generalizations of electromagnetic fields to higher dimensions. It has become clear recently that those are extremely important for the construction of realistic stringtheoretic models. The quantization conditions of RR fluxes on compact spaces imply discrete values of effective couplings and thus crucial for experimental verifications. RR fluxes are also an integral part of the AdS/CFT duality which relates strongly coupled gauge theories with weakly coupled dual models. To go beyond the supergravity approximation requires quantization of the string theory in the presence of a nontrivial RR background and has been studied in this project for higher correlation functions. This project succeeded in constructing a large number of new GUTs (Grand Unified Theories). These were made publicly available in a data base of over 30,000 models, which are of phenomenological interest given the current experimental search at CERN for physics beyond the standard model of particle physics.