DLCQ of M-Theory as the Light-Like Limit

TL;DR

This paper explores the possibility of defining DLCQ of M-theory as a limit of M-theory compactified on an almost light-like circle, providing perturbative and non-perturbative evidence for its well-defined nature.

Contribution

It demonstrates that both perturbative string amplitudes and certain non-perturbative states behave consistently in the light-like limit, supporting the existence of DLCQ for M-theory.

Findings

Perturbative string loop amplitudes have a finite light-like limit with proper external momenta.

Wrapped D-branes exhibit the correct light-like limit behavior.

Non-perturbative corrections may also behave appropriately in the light-like limit.

Abstract

We investigate whether DLCQ of M-theory can be defined as a limit of M-theory compactified on an almost light-like circle. This is of particular interest since the proofs of the matrix description of M-theory by Seiberg and Sen rely on this assumption. By the standard relation between M-theory on $S^1$ and IIA string theory, we translate this question into the corresponding one about the existence of the light-like limit of IIA superstring theory for any string coupling $g_s$. We argue that perturbative string loop amplitudes should have a finite and well-defined light-like limit provided the external momenta are chosen to correspond to a well-defined DLCQ set-up. On the non-perturbative side we consider states and amplitudes. We show that an appropriate class of non-perturbative states (wrapped D-branes) precisely have the right light-like limit. We give some indications that non-perturbative corrections to string amplitudes, too, may behave as required in the light-like limit. Having perturbative and non-perturbative evidence, this suggests that type IIA superstring theory as a whole has a well-defined light-like limit (for any string coupling $g_s$) and hence that the same is true for M-theory.