Superstring Amplitudes as a Mellin Transform of Supergravity

TL;DR

This paper establishes a mathematical correspondence between superstring and supergravity amplitudes, showing that superstring amplitudes can be expressed as Mellin transforms of supergravity amplitudes, revealing deep structural links between the theories.

Contribution

It introduces a novel superstring/supergravity correspondence by mapping vertex positions to helicity spinors and expressing superstring amplitudes as Mellin transforms of supergravity amplitudes.

Findings

Superstring amplitudes are Mellin transforms of supergravity amplitudes.

A mapping between vertex positions and helicity spinors is constructed.

Properties of Mellin transforms are elaborated within this correspondence.

Abstract

At the tree level, the maximally helicity violating amplitudes of N gauge bosons in open superstring theory and of N gravitons in supergravity are known to have simple representations in terms of tree graphs. For superstrings, the graphs encode integral representations of certain generalized Gaussian hypergeometric functions of kinematic invariants while for supergravity, they represent specific kinematic expressions constructed from spinor-helicity variables. We establish a superstring/supergravity correspondence for this class of amplitudes, by constructing a mapping between the positions of gauge boson vertices at the disk boundary and the helicity spinors associated to gravitons. After replacing vertex positions by a larger set of N(N-3)/2 coordinates, the superstring amplitudes become (multiple) Mellin transforms of supergravity amplitudes, from the projective space into the dual Mellin space of N(N-3)/2 kinematic invariants. Similarly, inverse Mellin transforms transmute open superstrings into supergravity. We elaborate on the properties of multiple Mellin and inverse Mellin transforms in the framework of superstring/supergravity correspondence.