Generalized Veneziano and Virasoro amplitudes

TL;DR

This paper investigates generalized Veneziano and Virasoro amplitudes, deriving recursion relations that constrain their spectra, and finds that the string spectrum uniquely satisfies the Virasoro case under certain assumptions.

Contribution

It introduces a framework for analyzing generalized amplitudes, solving the Veneziano case analytically, and establishing the uniqueness of the string spectrum in the Virasoro case.

Findings

Veneziano amplitudes form a two-parameter family including Coon amplitudes.

The Veneziano recursion relation admits an analytical solution.

The Virasoro case uniquely yields the string spectrum.

Abstract

We analyze so-called generalized Veneziano and generalized Virasoro amplitudes. Under some physical assumptions, we find that their spectra must satisfy an over-determined set of non-linear recursion relations. The recursion relation for the generalized Veneziano amplitudes can be solved analytically and yields a two-parameter family which includes the Veneziano amplitude, the one-parameter family of Coon amplitudes, and a larger two-parameter family of amplitudes with an infinite tower of spins at each mass level. In the generalized Virasoro case, the only consistent solution is the string spectrum.