Recursion Relations from Space-time Supersymmetry

TL;DR

This paper introduces a method to derive relations between higher derivative interactions in supersymmetric theories, applying it to string theory to analyze the coupling dependence and renormalization properties of specific interactions.

Contribution

It extends the derivation of relations between higher derivative interactions to all orders in momentum and applies supersymmetry to determine their behavior in string theory.

Findings

Interactions satisfy Poisson equations on moduli space

Protected couplings are only finitely renormalized

Implications for low k interactions analyzed

Abstract

We describe a method for obtaining relations between higher derivative interactions in supersymmetric effective actions. The method extends to all orders in the momentum expansion. As an application, we consider the string coupling dependence of the \hat{G}^{2k} \lambda^{16} interaction in type IIB string theory. Using supersymmetry, we show that each of these interactions satisfies a Poisson equation on the moduli space with sources determined by lower momentum interactions. We argue that these protected couplings are only renormalized by a finite number of string loops together with non-perturbative terms. Finally, we explore some consequences of the Poisson equation for low values of k.