Analyticity and Crossing Symmetry of Superstring Loop Amplitudes

TL;DR

This paper proves analyticity and crossing symmetry of superstring loop amplitudes directly in momentum space, extending foundational quantum field theory results to superstring theory at all perturbative orders.

Contribution

It establishes the analyticity properties of superstring Green's functions directly in momentum space, bypassing the need for position space properties, and applies to all orders in perturbation theory.

Findings

Proves analyticity of superstring Green's functions in momentum space.

Demonstrates crossing symmetry of superstring amplitudes.

Applicable to all orders in perturbation theory with regularization of massless particle effects.

Abstract

Bros, Epstein and Glaser proved crossing symmetry of the S-matrix of a theory without massless fields by using certain analyticity properties of the off-shell momentum space Green's function in the complex momentum plane. The latter properties follow from representing the momentum space Green's function as Fourier transform of the position space Green's function, satisfying certain properties implied by the underlying local quantum field theory. We prove the same analyticity properties of the momentum space Green's functions in superstring field theory by directly working with the momentum space Feynman rules even though the corresponding properties of the position space Green's function are not known. Our result is valid to all orders in perturbation theory, but requires, as usual, explicitly subtracting / regulating the non-analyticities associated with massless particles. These results can also be used to prove other general analyticity properties of the S-matrix of superstring theory.