Multiparticle one-loop amplitudes and S-duality in closed superstring theory

TL;DR

This paper computes explicit one-loop five-supergraviton amplitudes in type II superstring theories using pure spinor formalism, revealing new insights into S-duality effects on the effective action and amplitude structures.

Contribution

It provides explicit one-loop five-particle superstring amplitudes and explores their implications for S-duality and effective action terms, extending previous analyses.

Findings

Type IIB amplitude expressed as a doubling of super Yang--Mills tree amplitude.

Type IIA amplitude includes additional non-factorizable pieces.

S-duality acts on moduli-dependent coefficients, extending previous understanding.

Abstract

Explicit expressions for one-loop five supergraviton scattering amplitudes in both type II superstring theories are determined by making use of the pure spinor formalism. The type IIB amplitude can be expressed in terms of a doubling of ten-dimensional super Yang--Mills tree amplitude, while the type IIA amplitude has additional pieces that cannot be expressed in that manner. We evaluate the coefficients of terms in the analytic part of the low energy expansion of the amplitude, which correspond to a series of terms in an effective action of the schematic form D^{2k}R^5 for 0\le k \le 5 (where R is the Riemann curvature). Comparison with earlier analyses of the tree amplitudes and of the four-particle one-loop amplitude leads to an interesting extension of the action of SL(2,Z) S-duality on the moduli-dependent coefficients in the type IIB theory. We also investigate closed-string five-particle amplitudes that violate conservation of the U(1) R-symmetry charge -- processes that are forbidden in supergravity. The coefficients of their low energy expansion are shown to agree with S-duality systematics. A less detailed analysis is also given of the six-point function, resulting in the vanishing of the analytic parts of the R^6 and D^4 R^6 interactions in the ten-dimensional effective action, but not in lower dimensions.