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

Abstract

We analyse the contribution of $2n$ scalars to the Operator Product Expansion series for MHV gluon scattering amplitudes/polygonal Wilson loops in planar $\mathcal{N}=4$ 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.

arXiv comment12 pages, typos corrected, final comments and formula (implicit in the previous version) added, published version (Phys. Rev. D)

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• Pentagon OPE resummation in N=4 SYM: hexagons with one effective particle contribution
• Resummed tree heptagon
• Vacuum expectation value of twist fields
• Spectral determinants for twist field correlators
• Twisting perturbed parafermions
• $\mathcal{N}=4$ polygonal Wilson loops: fermions
• Hexagon Bootstrap in the Double Scaling Limit
• A Young diagram expansion of the hexagonal Wilson loop (amplitude) in $\mathcal{N}=4$ SYM