On Unitarity of the Hypergeometric Amplitude

TL;DR

This paper extends the hypergeometric deformation of the Veneziano amplitude to superstring theory, analyzing unitarity constraints and establishing positivity of partial wave coefficients in various parameter regimes.

Contribution

It constructs a hypergeometric generalization of the Veneziano amplitude for superstring theory and systematically analyzes unitarity and positivity constraints in the parameter space.

Findings

Identifies regions of parameter space where the amplitude is unitary.

Demonstrates positivity of partial wave coefficients in broader cases.

Rules out large non-unitary regions based on residue analysis.

Abstract

The hypergeometric amplitude is a one-parameter deformation of the Veneziano amplitude for four-point tachyon scattering in bosonic string theory that is consistent with $S$-matrix bootstrap constraints. In this article we construct a similar hypergeometric generalization of the Veneziano amplitude for type-I superstring theory. We then rule out a large region of the $(r,m^2,D)$ parameter space as non-unitary, and establish another large subset of the $(r, m^2, D)$ parameter space where all of the residue's partial wave coefficients are positive. We also analyze positivity in various limits and special cases. As a corollary to our analysis, we are able to directly demonstrate positivity of a wider set of Veneziano amplitude partial wave coefficients than what has been presented elsewhere.