Four Loop Scattering in the Nambu-Goto Theory

TL;DR

This paper explores multiloop scattering amplitudes in the Nambu-Goto string theory, revealing surprising polynomial behavior at two loops and the emergence of logarithmic dependencies at higher loops, linked to integrable models.

Contribution

It provides the first detailed calculation of multiloop scattering in Nambu-Goto theory and uncovers the role of (semi)integrability in amplitude structure.

Findings

On-shell amplitudes are polynomial at two loops despite UV counterterms.

At three loops, amplitudes develop non-polynomial (logarithmic) momentum dependence.

The approach bypasses brute force calculations for higher loops using integrability insights.

Abstract

We initiate the study of multiloop scattering amplitudes in the Nambu-Goto theory on the worldsheet of a non-critical string. We start with a brute force calculation of two loop four particle scattering. Somewhat surprisingly, even though non-trivial UV counterterms are present at this order, on-shell amplitudes remain polynomial in the momenta of colliding particles. We show that this can be understood as a consequence of existence of certain close by (semi)integrable models. Furthermore, these arguments can be extended to obtain the answer for three and four loop scattering, bypassing the brute force calculation. The resulting amplitudes develop non-polynomial (logarithmic) dependence on the momenta starting at three loops.