Strings, Supergravity, Geometry and Duality

String Theory is by now well established as a leading candidate for the description  of quantum gravity. Its simple premise is to replace point particles with strings, whose quantum excitations include a massless spin 2 mode; the putative graviton of quantum gravity. Indeed, in the low energy regime, general relativity, or its supersymmetric extension namely supergravity, provides an effective description of the string dynamics with the different solutions of supergravity corresponding to string theory vacua. However, in this pointparticle supergravity limit essential features of string theory are not captured. Most notably, the extended nature of strings and their ability to wind around a compact direction in spacetime gives rise to exciting and unexpected behavior that is in complete contrast to that of point particles.

A remarkable phenomenon, known as T-duality, is that seemingly different supergravity backgrounds can give equivalent string theories. In its simplest form, T-duality is the equivalence of strings on a circle of large radius R and those on small circle of radius α’/R (α’

is the square of the string length scale). T-duality interchanges string momenta and winding modes whilst modifying the geometry in such a way that the physics is left invariant. T-duality is just the tip of a much wider class of dualities in String Theory known as U-dualities, which paved the way to the idea of M-theory; an all-encompassing theory that unites all

of the different duality related regimes of string theory.

These dualities pose a fundamental question – do they have a geometrical underpinning? More precisely is there a more appropriate geometrical language in which to formulate string theory that takes into account the extended nature of the string and its dualities. The past few years have seen an upsurge in interest and understanding in addressing this, and related issues, with considerable advances on several fronts. The main themes of our research can be captured by:

• Generalized Geometry
• Double field theory/exceptional field theory (DFT/EFT)
• Doubled worldsheet formalisms
• Branes and backgrounds in DFT/EFT
• Generalized T-duality and their Applications
• T-duality and new integrable models