Some properties of the Alday-Maldacena minimum

TL;DR

This paper explores the properties of the Alday-Maldacena minimal surface solution in AdS space, compares it with Nambu-Goto solutions, and discusses implications for gluon scattering amplitudes in N=4 SYM at strong coupling.

Contribution

It introduces an analogous Nambu-Goto solution space, compares it with the Alday-Maldacena sigma-model solutions, and proposes a new function related to the five-gluon amplitude.

Findings

A Nambu-Goto solution space is constructed and compared to the Alday-Maldacena solution.

The intersection of sigma-model and Nambu-Goto moduli spaces is identified.

A function of moduli parameters reproduces the five-gluon amplitude, acting as a Legendre transform.

Abstract

The Alday-Maldacena solution, relevant to the n=4 gluon amplitude in N=4 SYM at strong coupling, was recently identified as a minimum of the regularized action in the moduli space of solutions of the AdS_5 sigma-model equations of motion. Analogous solutions of the Nambu-Goto equations for the n=4 case are presented and shown to form (modulo the reparametrization group) an equally large but different moduli space, with the Alday-Maldacena solution at the intersection of the sigma-model and Nambu-Goto moduli spaces. We comment upon the possible form of the regularized action for n=5. A function of moduli parameters z_a is written, whose minimum reproduces the BDDK one-loop five-gluon amplitude. This function may thus be considered as some kind of Legendre transform of the BDDK formula and has its own value independently of the Alday-Maldacena approach.