S and U-duality Constraints on IIB S-matrices

TL;DR

This paper proposes a constrained form for graviton scattering amplitudes in IIB superstring theory using automorphic functions, aligning with duality symmetries and perturbative data, and explores implications for supergravity finiteness.

Contribution

It introduces a novel functional form for graviton scattering amplitudes based on Eisenstein series, consistent with dualities, perturbative expansions, and unitarity, advancing understanding of IIB superstring theory.

Findings

Proposes a functional form compatible with duality symmetries and perturbative data.

Demonstrates a perturbative truncation in the genus expansion.

Suggests implications for the finiteness of supergravity theories.

Abstract

S and U-duality dictate that graviton scattering amplitudes in IIB superstring theory be automorphic functions on the appropriate fundamental domain which describe the inequivalent vacua of (compactified) theories. A constrained functional form of graviton scattering is proposed using Eisenstein series and their generalizations compatible with: a) two-loop supergravity, b) genus one superstring theory, c) the perturbative coupling dependence of the superstring, and d) with the unitarity structure of the massless modes. The form has a perturbative truncation in the genus expansion at a given order in the derivative expansion. Comparisons between graviton scattering S-matrices and effective actions for the first quantized superstring are made at the quantum level. Possible extended finiteness properties of maximally extended quantum supergravity theories in different dimensions is implied by the perturbative truncation of the functional form of graviton scattering in IIB superstring theory.