On the DLCQ as a light-like limit in string theory

TL;DR

This paper investigates the discrete light-cone quantization (DLCQ) in string theory, demonstrating that multi-loop scattering amplitudes are well-defined in the light-like limit, but vacuum amplitudes face divergences that supersymmetry may resolve.

Contribution

The authors construct multi-loop string scattering amplitudes using the KSV method and analyze their behavior in the light-like limit, clarifying the quantum-level issues of DLCQ.

Findings

Multi-loop scattering amplitudes are well-defined in the light-like limit.

Vacuum amplitudes are divergent due to zero-mode loops.

Supersymmetry may resolve divergences in vacuum amplitudes.

Abstract

We study the issue of defining the discrete light-cone quantization (DLCQ) in perturbative string theory as a light-like limit. While this limit is unproblematic at the classical level, it is non-trivial at the quantum level due to the divergences by the zero-mode loops. We reconsider this problem in bosonic string theory. We construct the multi-loop scattering amplitudes in both open and closed string theories by using the method of Kikkawa, Sakita and Virasoro (KSV), and then we show that these scattering amplitudes are perfectly well-defined in this limit. We also discuss the vacuum amplitudes of the string theory. They are, however, ill-defined in the light-like limit due to the zero-mode loop divergences, and hence we want supersymmetry to cure those pathological divergences even in string theory.