g-Functions and gluon scattering amplitudes at strong coupling

TL;DR

This paper analyzes gluon scattering amplitudes at strong coupling in N=4 super Yang-Mills theory by connecting minimal surface areas in AdS_3 with thermodynamic Bethe ansatz systems, providing explicit calculations and comparisons with 2-loop results.

Contribution

It introduces a novel approach to compute the remainder function using T- and Y-functions from the sine-Gordon model and CFT perturbation, linking boundary entropy to amplitude corrections.

Findings

Explicit expressions for 8- and 10-point amplitudes at the CFT point.

Good agreement between strong coupling and 2-loop formulas.

Power series structures of the rescaled remainder functions are similar.

Abstract

We study gluon scattering amplitudes/Wilson loops in N=4 super Yang-Mills theory at strong coupling by calculating the area of the minimal surfaces in AdS_3 based on the associated thermodynamic Bethe ansatz system. The remainder function of the amplitudes is computed by evaluating the free energy, the T- and Y-functions of the homogeneous sine-Gordon model. Using conformal field theory (CFT) perturbation, we examine the mass corrections to the free energy around the CFT point corresponding to the regular polygonal Wilson loop. Based on the equivalence between the T-functions and the g-functions, which measure the boundary entropy, we calculate corrections to the T- and Y-functions as well as express them at the CFT point by the modular S-matrix. We evaluate the remainder function around the CFT point for 8 and 10-point amplitudes explicitly and compare these analytic expressions with the 2-loop formulas. The two rescaled remainder functions show very similar power series structures.