Superstring Amplitudes, Unitarity, and Hankel Determinants of Multiple Zeta Values

TL;DR

This paper explores how unitarity and analyticity impose positivity constraints on superstring scattering amplitudes, revealing new mathematical relations involving Hankel determinants of multiple zeta values.

Contribution

It introduces positivity constraints on Hankel determinants of multiple zeta values in superstring amplitudes, generalizing known results from single zeta values.

Findings

Positivity constraints on Hankel determinants derived from superstring amplitudes.

Generalization of mathematical constraints on zeta value polynomials.

Connections between unitarity, analyticity, and multiple zeta values.

Abstract

The interplay of unitarity and analyticity has long been known to impose strong constraints on scattering amplitudes in quantum field theory and string theory. This has been highlighted in recent times in a number of papers and lecture notes. Here we examine such conditions in the context of superstring tree-level scattering amplitudes, leading to positivity constraints on determinants of Hankel matrices involving polynomials of multiple zeta values. These generalise certain constraints on polynomials of single zeta values in the mathematics literature.