HIgher Polylogarithms and String AMplitudes

ended

In this interdisciplinary project we will describe the mathematical structure of superstring amplitudes in genus one and two, generalizing recent beautiful progress made at genus zero. This will enable us to present original ideas for advancing in the study of higher-genus polylogarithms, and at the same time to obtain new information on string theory predictions for fundamental interactions. To reach our goal, we will focus on three main research directions, and we will collaborate with some of the world-leading experts on the subject, among which my host supervisor P. Vanhove. In particular, we will complete the description of genus-one superstring amplitudes in terms of elliptic polylogarithms, we will begin a systematic analysis of the special functions involved at genus two and we will push the computation of the low-energy expansion of closed-string amplitudes. Parts of this project will require advanced tools from algebraic geometry, which we plan to discuss with the secondment supervisor F. Brown at University of Oxford. The Theoretical Physics Institute (IPhT, Saclay) of CEA (host institution) is one of the few places in Europe hosting international experts in all branches of mathematical physics related to the topic of this proposal. The results obtained will point towards new directions in many fields of mathematics, such as mixed motives and moduli spaces of curves, opening new research gates completely inspired by physics. On the other side, the techniques developed will allow to attack similar nowadays intractable computations of amplitudes in quantum field theory, which can be compared with the experimental data produced by particle accelerators.