Twistor Inspired Techniques For Perturbative Gauge Theory

In science, it is the detailed quantitative comparison between theories and experimental results which often leads to new discoveries and improvements in our understanding of nature. In 2007, a major new experiment-the Large Hadron Collider or LHC will commence operation. This experiment is the culmination of twenty years of design, planning and construction. It will probe new energy regimes of physics and has tremendous potential for discovering new physics. These discoveries may be very obvious or may only become clear when we compare the experimental findings with the detailed predictions of our existing theories. Unfortunately, within some of our favoured theories-gauge theories- the computation of these predictions is extremely complicated. This complication is a genuine technical barrier which currently prohibits us from giving accurate predictions. This project is about improving our technical resources for determining the predictions of gauge theories. We aim to use strange mathematical links, or dualities, betwen gauge theories and other problems which allow us to make use a different view of the calculation. Hopefully, we will be able to use these dualities to develope new calculational techniques. Of course new techniques can have more than one application. In addition to calculating amplitudes of interest to LHC we also intend applying these to some outstanding problems in quantum gravity. The quantum consistency of pure Einstein gravity has been settled some years ago. (It is not consistent!) However there are modifications of Einstein gravity, where gravity is combined with other forces and with very specific forms of matter, whose quantum consistency is unclear. We intend to apply our techniques to calculate amplitudes in these so-called ``maximally supersymmetric'' theories of gravity to either find quantum inconsistencies or attempt to prove these theories are consistent quantum theories of gravity.