String theory, gauge theory and duality

While particle theories of the microscopic world have long been known to work by the rules of quantum mechanics, gravity is described by Einstein's geometry of spacetime. Unifying the two, in order to provide a complete picture that applies just as well to matter falling into black holes as to the earliest history of the universe, has been the outstanding challenge of theoretical physics. String theory in the seventies and eighties made important progress on the problem of unifying quantum particles with gravity. It also offers new insights into generalisations of Einstein's geometry and novel technical tools to understand the gluons of particle physics. It challenges the very heart of the apparent dichotomy between quantum particle physics and geometrical gravity, replacing it with the new paradigm of gauge-string duality. The consequences of the unification are predictions about our world, such as the existence of extra-dimensions. However, many crucial questions are still open today, e.g exactly how small is the string and precisely which of the many solutions of string theory is relevant in going beyond the standard model of particle physics. Upcoming high energy experiments at the LHC will provide vital clues. Work at Queen Mary will study particular string solutions and will extract their interactions. Since string theory incorporates gravity, it also provides one theoretical framework for experiments in cosmology eg with regard to the cosmic microwave background. Our work will include studies of inflation in the early history of the universe in terms of extended objects, called D-branes. One of the remarkable geometrical insights of string theory, discovered in the nineties, was that the ten dimensions of stringy spacetime hide an extra dimension. This extra dimensional geometry underlying string theory, often studied under the name of M-theory, is the subject of past and ongoing research here. There are hints that fuzzy geometry, where spacetime coordinates do not behave like ordinary numbers, plays a role in the branes of M-theory. This is the beginning of a fascinating story which our future research aims to unravel. Another extension of Einstein's theory which we will study involves doubled geometry, where the windings of the string and their centre of mass motion are treated symmetrically. In the eighties, gluons were found to have remarkably simple scattering probabilities, which were previously unsuspected. Work in the last four years revealed that the source of the hidden simplicity was a string theory in twistor space. The Queen Mary group discovered that twistor string ideas work well, even when the gluons are allowed to interact through complicated loops. The twistor string has led to many new theoretical methods for calculating scattering amplitudes. These will be applied to an extended class of particle theories, and will strengthen the theoretical tools available to calculate the amplitudes relevant to the Large Hadron Collider. Very recently it has also been shown how to use gauge-string duality to calculate scattering. We have described how this works in the quantum theory in certain cases, and this will be generalised. Gauge-string duality emerged in the nineties from the study of D-branes in stringy spacetime. This duality is a surprising equivalence between non-gravitational quantum particle (gauge) theories on the one hand and quantum gravitational stringy theories on the other. Members of the QM group have pioneered the application of a class of purely mathematical dualities, which appear in the theory of symmetries, to the gauge-string duality of theoretical physics.The proposed work will build on this to shed further light on spacetime gravitational phenomena such as giant gravitons and black holes. We will use gauge-string duality to study the harder questions of quantum gravity, such as black hole dynamics and early cosmology.