The contribution of scalars to ${\cal N}=4$ SYM amplitudes

TL;DR

This paper investigates how scalars contribute to gluon scattering amplitudes in planar ${ m N}=4$ SYM, revealing that their effects grow with coupling and can rival classical contributions, with explicit large-coupling formulas provided.

Contribution

It introduces a novel analysis of scalar contributions to amplitudes, including explicit large-coupling expressions and a new method using Young tableaux for all couplings.

Findings

Scalar contributions grow with coupling, competing with classical terms.

Explicit formulas for two and four scalars at large coupling.

A new approach using Young tableaux for all coupling regimes.

Abstract

We analyse the contribution of $2n$ scalars to the Operator Product Expansion series for MHV gluon scattering amplitudes/polygonal Wilson loops in planar ${\cal N}=4$ SYM. Hence, we sum up on $2n$ for large coupling $\lambda$: the logarithm of the amplitude is proportional to $\sqrt{\lambda}$, thus competing, unexpectedly, with the famous classical contribution. We give explicit expressions for the first terms at large $\lambda$ in case of two and four scalars. For finalising this analysis, we find profitable an explicit computation of the $2n$-scalar term at any coupling by means of Young tableaux, paralleling, under certain aspects, the Nekrasov-Okounkov expressions for $\mathcal N =2$ SYM prepotential.