2-loop scattering on superstring and supermembrane in flat space

TL;DR

This paper calculates the 2-loop scattering amplitudes of superstring and supermembrane in flat space, showing finiteness in superstring but divergences in supermembrane, highlighting differences in their quantum properties.

Contribution

It provides the first detailed 2-loop analysis of superstring and supermembrane scattering amplitudes, revealing finiteness in superstring and divergences in supermembrane.

Findings

Superstring 2-loop S-matrix is finite and free of non-trivial UV divergences.

Supermembrane exhibits genuine 2-loop UV divergences, indicating non-finiteness.

Results support the integrability of the superstring model and highlight the non-finiteness of the supermembrane.

Abstract

We consider the S-matrix of transverse scalar excitations on an infinite $D=10$ GS superstring and $D=11$ supermembrane in flat target space. We compute the 4-particle scattering amplitude in the 2-loop approximation and demonstrate that, like in the Nambu string case, the $D=10$ GS string S-matrix does not contain non-trivial 2d UV divergences (UV pole not accompanied by terms with logarithms of momenta is an artifact of dimensional regularization). This is consistent with underlying integrability of this model which is maintaining by adding appropriate local counterterms. In the supermembrane case there are no 1-loop divergences but we find a genuine 2-loop UV pole. This demonstrates non-finiteness of the world-volume S-matrix of the M2 brane theory.