Quantum Wronskian approach to six-point gluon scattering amplitudes at strong coupling

TL;DR

This paper develops a quantum Wronskian approach to analyze six-point gluon scattering amplitudes at strong coupling in N=4 super Yang-Mills theory, deriving new analytic expansions and comparing with perturbative results.

Contribution

It introduces a novel quantum Wronskian method within an integrable model framework to study scattering amplitudes at strong coupling, providing new analytic expansions and insights.

Findings

Derived the TBA equations and functional relations for the model.

Obtained the leading analytic expansion of the remainder function.

Found strong coupling results closely match multi-loop perturbative results.

Abstract

We study the six-point gluon scattering amplitudes in N=4 super Yang-Mills theory at strong coupling based on the twisted Z_4-symmetric integrable model. The lattice regularization allows us to derive the associated thermodynamic Bethe ansatz (TBA) equations as well as the functional relations among the Q-/T-/Y-functions. The quantum Wronskian relation for the Q-/T-functions plays an important role in determining a series of the expansion coefficients of the T-/Y-functions around the UV limit, including the dependence on the twist parameter. Studying the CFT limit of the TBA equations, we derive the leading analytic expansion of the remainder function for the general kinematics around the limit where the dual Wilson loops become regular-polygonal. We also compare the rescaled remainder functions at strong coupling with those at two, three and four loops, and find that they are close to each other along the trajectories parameterized by the scale parameter of the integrable model.