Finiteness and Unitarity of Lorentz-Covariant Green-Schwarz Superstring Amplitudes

TL;DR

This paper introduces a new method for calculating ten-dimensional superstring amplitudes that are manifestly Lorentz-invariant, finite, and unitary, advancing the understanding of superstring theory's consistency.

Contribution

It develops a novel approach to compute superstring amplitudes with arbitrary loops and external particles, ensuring Lorentz invariance, finiteness, and unitarity.

Findings

Amplitudes are explicitly shown to be finite by analyzing Riemann surface degenerations.

Amplitudes are proven to be unitary through comparison with light-cone formalism.

The method applies to arbitrary loop orders and external massless particles.

Abstract

In two recent papers, a new method was developed for calculating ten-dimensional superstring amplitudes with an arbitrary number of loops and external massless particles, and for expressing them in manifestly Lorentz-invariant form. By explicitly checking for divergences when the Riemann surface degenerates, these amplitudes are proven to be finite. By choosing light-cone moduli for the surface and comparing with the light-cone Green-Schwarz formalism, these amplitudes are proven to be unitary.