T-functions and multi-gluon scattering amplitudes

TL;DR

This paper explores the computation of gluon scattering amplitudes in N=4 super Yang-Mills theory at strong coupling, expressing the remainder function via T-functions from the TBA system, and comparing results with two-loop calculations.

Contribution

It provides a concise expression of the remainder function in terms of T-functions and derives a leading-order expansion for general 2n-point functions, connecting strong coupling results with perturbative calculations.

Findings

The remainder function can be expressed using T-functions from the TBA system.

The leading-order expansion formula for the 2n-point remainder function is derived.

Rescaled remainder functions at strong coupling and two loops are close, with a ratio near 0.9 for large n.

Abstract

We study gluon scattering amplitudes/Wilson loops in N=4 super Yang-Mills theory at strong coupling which correspond to minimal surfaces with a light-like polygonal boundary in AdS_3. We find a concise expression of the remainder function in terms of the T-function of the associated thermodynamic Bethe ansatz (TBA) system. Continuing our previous work on the analytic expansion around the CFT/regular-polygonal limit, we derive a formula of the leading-order expansion for the general 2n-point remainder function. The T-system allows us to encode its momentum dependence in only one function of the TBA mass parameters, which is obtained by conformal perturbation theory. We compute its explicit form in the single mass cases. We also find that the rescaled remainder functions at strong coupling and at two loops are close to each other, and their ratio at the leading order approaches a constant near 0.9 for large n.