Recurrence Relations of Higher Spin BPST Vertex Operators for Open String

TL;DR

This paper derives recurrence relations for higher spin BPST vertex operators in open bosonic string theory, connecting these to recent findings on Regge string scattering amplitudes, and expresses the operators using Kummer functions.

Contribution

It introduces a method to express higher spin BPST vertex operators via Kummer functions and derives infinite recurrence relations among them, linking to Regge scattering amplitudes.

Findings

Recurrence relations among BPST vertex operators are established.

These relations lead to recurrence relations among Regge string scattering amplitudes.

Operators are expressed in terms of Kummer functions of the second kind.

Abstract

We calculate higher spin BPST vertex operators for open bosonic string and express these operstors in terms of Kummer function of the second kind. We derive infinite number of recurrence relations among BPST vertex operators of different string states. These recurrence relations among BPST vertex operators lead to the recurrence relations among Regge string scattering amplitudes discovered recently.