Complete N-Point Superstring Disk Amplitude II. Amplitude and Hypergeometric Function Structure

TL;DR

This paper analyzes the structure of hypergeometric functions in superstring amplitudes, revealing their relations to monodromy, basis structures, and properties like poles and transcendentality, advancing understanding of string effects in gauge theories.

Contribution

It provides a detailed analysis of the hypergeometric functions in superstring amplitudes, including their monodromy relations, basis structures, and algebraic properties, building on previous amplitude computations.

Findings

Hypergeometric functions relate to monodromy equations.

A minimal basis structure for hypergeometric functions is identified.

Methods to determine poles and transcendentality are proposed.

Abstract

Using the pure spinor formalism in part I [1] we compute the complete tree-level amplitude of N massless open strings and find a striking simple and compact form in terms of minimal building blocks: the full N-point amplitude is expressed by a sum over (N-3)! Yang-Mills partial subamplitudes each multiplying a multiple Gaussian hypergeometric function. While the former capture the space-time kinematics of the amplitude the latter encode the string effects. This result disguises a lot of structure linking aspects of gauge amplitudes as color and kinematics with properties of generalized Euler integrals. In this part II the structure of the multiple hypergeometric functions is analyzed in detail: their relations to monodromy equations, their minimal basis structure, and methods to determine their poles and transcendentality properties are proposed. Finally, a Groebner basis analysis provides independent sets of rational functions in the Euler integrals.