Compactification in the Lightlike Limit

TL;DR

This paper investigates the behavior of field theories as a compactified dimension approaches a lightlike limit, revealing divergence issues in perturbation theory and discussing nonperturbative existence and implications for matrix theory.

Contribution

It provides a detailed analysis of the divergences in perturbative amplitudes and explores the nonperturbative existence of the lightlike limit, with implications for matrix theory.

Findings

Perturbative amplitudes diverge in the lightlike limit due to zero mode interactions.

The lightlike limit exists nonperturbatively despite perturbative divergences.

Implications for the matrix theory conjecture are discussed.

Abstract

We study field theories in the limit that a compactified dimension becomes lightlike. In almost all cases the amplitudes at each order of perturbation theory diverge in the limit, due to strong interactions among the longitudinal zero modes. The lightlike limit generally exists nonperturbatively, but is more complicated than might have been assumed. Some implications for the matrix theory conjecture are discussed.