MHV amplitudes at strong coupling and linearized TBA equations

Abstract

The maximally helicity violating (MHV) amplitudes of $\mathcal{N}=4$ 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.

41 pages, 9 figures; (v2) a reference added, typos corrected, minor revisions

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Cited by in corpus (6)

• The Origin of the Six-Gluon Amplitude in Planar $\mathcal{N}=4$ SYM
• Fermions and scalars in $\mathcal{N}=4$ Wilson loops at strong coupling and beyond
• TBA-like equations for non-planar scattering amplitude/Wilson lines duality at strong coupling
• An Origin Story for Amplitudes
• ABJM flux-tube and scattering amplitudes
• A Young diagram expansion of the hexagonal Wilson loop (amplitude) in $\mathcal{N}=4$ SYM