Superstring/Supergravity Mellin Correspondence in Grassmannian Formulation

TL;DR

This paper extends the Mellin correspondence between supergravity and superstring amplitudes to arbitrary helicity configurations using Grassmannian formulations, linking amplitudes to hypergeometric functions and contour integrations.

Contribution

It generalizes Hodges' determinant and establishes a new Grassmannian-based framework for supergravity and superstring amplitude correspondence.

Findings

Tree-level supergravity amplitudes derived from contour integrations in Grassmannians.

Superstring amplitudes expressed as hypergeometric functions of Mandelstam invariants.

Unified Grassmannian formulation for supergravity and superstring amplitudes.

Abstract

We extend the recently established Mellin correspondence of supergravity and superstring amplitudes to the case of arbitrary helicity configurations. The amplitudes are discussed in the framework of Grassmannian varieties. We generalize Hodges' determinant to a function of two sets of independent coordinates and show that tree-level supergravity amplitudes can be obtained by contour integrations of both sets in separate Grassmannians while in superstring theory, one set of coordinates is identified with string vertex positions at the disk boundary and Mellin transformed into generalized hypergeometric functions of Mandelstam invariants.