Strings, Supergravity, Geometry and Duality
The extended nature of strings allows for rather a surprising property: dualities which relate seemingly completely different regimes. The simplest example, T-duality, is that a circle of large radius R is indistinguishable from a small circle of radius 1/R from the point of view of a string. This remarkable phenomenon shows that conventional geometrical notions relevant for point particles may not be the natural geometry of space time as experienced by strings. One aspect of our work is to understand string theory in terms of a new geometrical approach, known as ”generalised” or ”doubled” geometry, that is adapted to strings and which promotes duality to a governing role. A further key aspect of our research in this area is to identify new types of duality in string theory, for instance how T-duality of circles can be extended to spaces with larger symmetries such as spheres and to understand applications of these dualities. We have led work on non-Abelian T-duality showing how it can be used within supergravity as a powerful solution generating technique. This has led to the identification of new classes of supersymmetric supergravity backgrounds that have interpretations as holographic duals of quantum field theories. We have explored how formal aspects of geometry e.g. G-structures can encode physical concepts such as confinement and symmetry breaking. More recent developments in this area have included the study of the relation between a class of two-dimensional integrable systems and non-Abelian T-duality.
Moduli stabilization, the AdS-CFT correspondence and string phenomenology all require the study of strings in non-trivial backgrounds. The method of choice to do so uses the supergravity approximation. In order to go beyond supergravity one is currently forced to use d = 2 conformal field theories, Landau-Ginzburg type descriptions, the pure spinor formalism or the σ-model worldsheet description. Particularly interesting are the non-linear σ-models in two dimensions with N = (2, 2) supersymmetry which highlight the rich interplay between string theory, supersymmetry and the mathematics of generalised Kahler and Calabi-Yau geometries. Recent work of the group in this area has included the study of D-branes in the context of the N=2 supersymmetric string world sheet, the description of the generalised geometry of supersymmetric Wess-Zumino-Witten models, and the study of supersymmetric chiral bosons.