Scattering on the supermembrane

Abstract

We compute the one-loop $2\to 2$ scattering amplitude of massless scalars on the world volume of an infinite $D=11$ supermembrane quantized in the static gauge. The resulting expression is manifestly finite and turns out to be much simpler than in the bosonic membrane case in arXiv:2308.12189 being simply proportional to the tree-level scattering amplitude. We also consider the case of ${\mathbb{R}}^{1,1}\times S^1$ membrane with one dimension compactified on a circle of radius R and demonstrate how the supermembrane scattering amplitude reduces to the one on an infinite $D=10$ Green-Schwarz superstring in the limit of R $\to 0$.

28 pages, v5: few signs corrected, footnote added