Equivalence of Two Contour Prescriptions in Superstring Perturbation Theory

TL;DR

This paper proves that two different methods for defining superstring perturbation amplitudes are equivalent, ensuring the consistency of the world-sheet approach with unitarity and resolving divergence issues at high energies.

Contribution

It establishes the equivalence of two contour deformation prescriptions in superstring perturbation theory, confirming the unitarity of the world-sheet approach.

Findings

Two prescriptions for superstring amplitudes are equivalent to all orders.

The equivalence confirms the unitarity of the world-sheet approach.

Addresses divergence issues at high energies in superstring theory.

Abstract

Conventional superstring perturbation theory based on the world-sheet approach gives divergent results for the S-matrix whenever the total center of mass energy of the incoming particles exceeds the threshold of production of any final state consistent with conservation laws. Two systematic approaches have been suggested for dealing with this difficulty. The first one involves deforming the integration cycles over the moduli space of punctured Riemann surfaces into complexified moduli space. The second one treats the amplitude as a sum of superstring field theory Feynman diagrams and deforms the integration contours over loop energies of the Feynman diagram into the complex plane. In this paper we establish the equivalence of the two prescriptions to all orders in perturbation theory. Since the second approach is known to lead to unitary amplitudes, this establishes the consistency of the first prescription with unitarity.