Is Physics in the Infinite Momentum Frame Independent of the Compactification Radius?

TL;DR

This paper investigates whether physical amplitudes in the infinite momentum frame are independent of the compactification radius, finding that in most cases they are, which supports the idea that Matrix theory describes uncompactified M-theory.

Contribution

It demonstrates that in the IMF, scattering amplitudes become independent of the compactification radius for both point particles and extended objects, with implications for M-theory.

Findings

Scattering amplitudes are R-independent in the IMF for point particles.

One-loop string amplitudes coincide with uncompactified theory in the IMF.

No exceptional processes with zero longitudinal momentum transfer in string case.

Abstract

With the aim of clarifying the eleven dimensional content of Matrix theory, we examine the dependence of a theory in the infinite momentum frame (IMF) on the (purely spatial) longitudinal compactification radius R. It is shown that in a point particle theory the generic scattering amplitude becomes independent of R in the IMF. Processes with zero longitudinal momentum transfer are found to be exceptional. The same question is addressed in a theory with extended objects. A one-loop type II string amplitude is shown to be R-independent in the IMF, and to coincide with that of the uncompactified theory. No exceptional processes exist in this case. The possible implications of these results for M-theory are discussed. In particular, if amplitudes in M-theory are independent of R in the IMF, Matrix theory can be rightfully expected (in the N -> infty limit) to describe uncompactified M-theory.