Comment on the Alday-Maldacena solution in calculating scattering amplitude via AdS/CFT

TL;DR

This paper clarifies the uniqueness of the Alday-Maldacena solution for strong coupling scattering amplitudes in N=4 SYM via AdS/CFT by imposing Virasoro constraints, resolving previous ambiguities.

Contribution

It demonstrates that imposing all Virasoro constraints yields a unique solution matching Alday-Maldacena's, addressing the moduli space issue in four-point scattering.

Findings

The solution is identical to Alday-Maldacena's for four-gluon scattering.

Imposing Virasoro constraints ensures solution uniqueness.

Resolves the moduli space ambiguity in four-point solutions.

Abstract

Following the recent proposal of Alday and Maldacena to obtain the strong coupling scattering amplitude in N=4 SYM via AdS/CFT, we point out that a unique solution can be obtained by imposing all the Virasoro constraints. In the case of four-gluon scattering, this solution is identical to the Alday-Maldacena solution, which is in accordance with the ansatz of Bern, Dixon and Smirnov. This also solves the moduli space problem of the four-point solution in a recent paper of Mironov, Morozov and Tomaras.