Gauge Theory Amplitudes and String Theory in Twistor Space

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One of the ultimate goals of modern theoretical physics is to discover the Theory of Everything, that is a unified description for the four apparently different forces we observe in nature: electromagnetic, weak, strong, and finally gravitational. In the 1970s, a theoretical framework was proposed which accomplishes the task of incorporating electromagnetism and the weak and strong force into a unified theory, the so-called Standard Model of fundamental interactions. This theory has passed many remarkable experimental tests, and has been studied in great detail thanks to powerful colliders, where particles are scattered at very high energy to study their interactions.Of the four fundamental forces of nature, gravity is the one we have the most experience of. It is however gravity which has escaped all attempts to be unified with the others for the longest time. Furthermore, and perhaps surprisingly, of all coupling constants - the number which, roughly speaking, quantifies the strength of the force - Newton's constant (related to the strength of gravity) is by far the smallest and also the one which is known with the smallest experimental precision. At present, there is only one theory which incorporates gravity with the forces of the Standard Model: this is String Theory. A musical analogue is appropriate here: When we hit a piano string, we not only produce the fundamental sound but also an infinite series of (less perceivable) overtones, or harmonics. In string theory, each harmonic corresponds to a different particle. Different harmonics have of course increasing frequency, and Quantum Mechanics taught us that frequency is proportional to energy. Energy is also related to mass, through Einstein's famous formula E=mc^2. Therefore all the particles in this infinite tower have an increasing mass.Actually string theory was discovered in a slightly different unification attempt. In the 1960s, a vast proliferation of particles had been discovered at particle colliders. Physicists tried to find an explanation for this mysterious fact, and thought that a theory of strings, with its infinite tower of particles, could be the solution to the puzzle. Representing a particle as the excitation of a string - an object with an intrinsic length - is a very different picture compared to the traditional concept of a particle as a pointlike object that we have been accustomed to since the time of Democritus. So it seems that we have two very different descriptions for the same object. What physicists realised in the last 30 years or so, is that many aspects of the interactions of particles can also be described by either resorting to the concept of point particle or to the alternative string description. The existence of two alternative descriptions is referred to as a duality between them.One could then ask why we need many descriptions of the same phenomena. Are we not satisfied with one, possibly the conventional one in terms of point particles, which seems to work pretty well? There are many possible answers to this objection. Firstly, having several different description of the same phenomenon leads inevitably to a deeper understanding of the phenomenon itself. Secondly, these different descriptions can be complementary, in the sense that one might work where the other fails. Another answer, directly relevant to this research project, is that the conventional approach of point particles (or Field Theory, in mathematical language) does not always account for the marvellous and unexpected simplicity of certain scattering amplitudes - quantities that physicists compute and can be measured experimentally at particle colliders. Unexplained beauty in mathematical formulae describing physical observables is often the hint of some deeper mathematical structure to be uncovered; string theory often plays the role of that deeper structure. By identifying new, simpler descriptions of known phenomena, we also gain a great deal in terms of computational power. This is crucial if we wish to discover new physics, which requires us to disentangle genuinely new phenomena from the processes due to Standard Model physics with great experimental precision. Edward Witten has recently discovered an example of duality which promises to be directly relevant for future experiments. It has already made it possible to dramatically increase our ability to compute phenomenologically interesting quantities. The study of this fascinating new duality, both on the field theory and on the string theory side, is the subject of my research proposal.