Duong H. Phong

Abstract:   In string theory, Feynman rules correspond to a volume form over the moduli space of Riemann surfaces. In genus > 1, the problem of determining Feynman rules had remained intractable to this day because of the presence of "supermoduli", and natural ansatze for the desired volume form had been plagued with ambiguities. In this talk, we show that these earlier problems can be traced back to gauge-fixing procedures which did not respect supersymmetry. For genus 2, we show that a proper gauge-fixing procedure produces new subtle contributions which eliminate all the earlier ambiguities: the resulting formula is independent of the choice of gauge slice. It can be rewritten in terms of modular forms. The cosmological constant is shown to vanish, and we also derive explicit formulas for the scattering of up to 4 gravitons.