2014/01/31 by Boris Pioline · 1 citation
Physics and Astronomy · #hep-th
paper · pdf · doi:10.1090/pspum/088/01457
published as Proc.Symp.Pure Math. 88 (2014) 119-144 · 24 pages, contribution to the proceedings of String-math 2013; v2: minor corrections and improvements, especially in section 4, more references
arxiv created 2014/07/10 · arxiv updated 2018/01/22
After integrating over supermoduli and vertex operator positions, scattering amplitudes in superstring theory at genus h≤ 3 are reduced to an integral of a Siegel modular function of degree h on a fundamental domain of the Siegel upper half plane. A direct computation is in general unwieldy, but becomes feasible if the integrand can be expressed as a sum over images under a suitable subgroup of the Siegel modular group: if so, the integration domain can be extended to a simpler domain at the expense of keeping a single term in each orbit -- a technique known as the Rankin-Selberg method. Motivated by applications to BPS-saturated amplitudes, Angelantonj, Florakis and I have applied this technique to one-loop modular integrals where the integrand is the product of a Siegel-Narain theta function times a weakly, almost holomorphic modular form. I survey our main results, and take some steps in extending this method to genus greater than one.