Does DLCQ S-matrix have a covariant continuum limit?

TL;DR

This paper demonstrates that the Discrete Light-Cone Quantization (DLCQ) S-matrix lacks a covariant continuum limit for certain processes, highlighting the complex role of zero modes in DLCQ and their impact on non-perturbative approaches.

Contribution

The authors develop a systematic perturbation theory for DLCQ and reveal the limitations of its covariant continuum limit, especially concerning zero mode contributions.

Findings

DLCQ S-matrix does not have a covariant continuum limit for $p^+=0$ exchange processes.

Zero modes play a more subtle role in DLCQ than previously understood.

Implications for non-perturbative approaches and brief comments on string theory DLCQ.

Abstract

We develop a systematic DLCQ perturbation theory and show that DLCQ S-matrix does not have a covariant continuum limit for processes with $p^+=0$ exchange. This implies that the role of the zero mode is more subtle than ever considered in DLCQ and hence must be treated with great care also in non-perturbative approach. We also make a brief comment on DLCQ in string theory.