MHV amplitudes at strong coupling and linearized TBA equations

TL;DR

This paper derives analytic expansions for 6-point MHV amplitudes in N=4 super Yang-Mills theory at strong coupling by solving linearized TBA equations, revealing differences from 2-loop results in certain kinematic regimes.

Contribution

It introduces a linearized TBA approach to analytically approximate MHV amplitudes at strong coupling, extending understanding of amplitude behavior in specific kinematic limits.

Findings

Derived analytic expansions valid for small conformal cross-ratios.

Found that strong coupling and 2-loop remainder functions differ significantly in certain regimes.

Provided leading power corrections to the amplitude expansions.

Abstract

The maximally helicity violating (MHV) amplitudes of ${\cal N} =4$ super Yang-Mills theory at strong coupling are obtained by solving auxiliary thermodynamic Bethe ansatz (TBA) integral equations. We consider a limit where the TBA equations are linearized for large chemical potentials and masses therein. By solving the linearized equations, we derive analytic expansions of the 6-point MHV amplitudes in terms of the ratio of the chemical potential $A$ and the mass $M$. The expansions are valid up to corrections exponentially small in $A$ or inversely proportional to powers of $A$. The analytic expansions describe the amplitudes for small conformal cross-ratios of the particle momenta in a standard basis, and interpolate the amplitudes with equal cross-ratios and those in soft/collinear limits. The leading power corrections are also obtained analytically. We compare the 6-point rescaled remainder functions at strong coupling and at 2 loops for the above kinematics. They are rather different, in contrast to other kinematic regions discussed in the literature where they are found to be similar to each other.