Generalised dualities in M-theory (FWOTM1032)

The outstanding challenge of theoretical physics is to find the ultimate description of the laws of nature, valid at all scales and energies, and unifying quantum theory with gravity. String theory is the most compelling candidate for such a theory. Strings are extended objects, and so behave very differently to elementary particles, which can only probe the universe one point at a time. This leads to a spectrum of unexpected "dualities'' that tell us very different string theory models are in fact the same, and point the way to the existence of a more fundamental description containing not only strings but other extended objects, all of which are transformed into each by duality. A full formulation of this underlying theory, termed M-theory, remains elusive. The presence of dualities seems to underly much of the complex mathematical structure of M-theory. Studying the structure and origin of dualities may provide hints towards a better understanding. Recently, new clues have appeared via a novel geometrical approach to M-theory, including the possibility that more general versions of known dualities exist. In my project, I will obtain new results about the fundamental physics of M-theory, using these generalised duality symmetries. I will investigate and classify the underlying geometrical and algebraic structure of these dualities, generate novel solutions of the theory, and explore the origin of such symmetries in terms of the fundamental extended objects of Mtheory

Keywords:Dualities, geometry, M-theory

Disciplines:High energy physics, Theoretical particle physics, Geometric aspects of physics, Field theory and string theory