Is physics in the infinite momentum frame independent of the compactification radius?

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 ppurely 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 uncompantified 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 → ∞ limit) to describe uncompactified M-theory.