Type IIB $R^4 H^{4g-4}$ Conjectures

TL;DR

This paper proposes conjectures for specific string coupling terms in Type IIB string theory, extending previous models and providing checks against known multiloop amplitudes, with applications to string production in background fields.

Contribution

It introduces $SL(2,Z)$ and $SL(3,Z)$ invariant conjectures for higher-order couplings in Type IIB strings, generalizing earlier conjectures and matching known multiloop results.

Findings

Conjectures reproduce multiloop amplitudes at weak coupling.

Extensions to $(p,q)$ string production in background $H$ fields.

Provides a framework for understanding higher-order couplings in string theory.

Abstract

We propose $SL(2,Z)$ (and $SL(3,Z)$) invariant conjectures for all $R^4 H^{4g-4}$ couplings of Type IIB strings on $R^{10}$ (and $R^{8}\times T^2$), generalizing conjectures of Green and Gutperle (and Kiritsis and Pioline) for the $R^4$ coupling. A strong check for our conjectures is that on $T^2$ at weak coupling, they reproduce the multiloop scattering amplitudes which had been previously computed using N=2 strings in the N=4 topological formalism. Applications to $(p,q)$ string production in a background $H$ field, generalizing Schwinger's computation for pair production in constant $F$ field, are suggested.