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.

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

References in corpus (5)

• Gluon scattering amplitudes at strong coupling
• Comments on operators with large spin
• An Operator Product Expansion for Polygonal null Wilson Loops
• On the collinear limit of scattering amplitudes at strong coupling
• Strong coupling for planar $\mathcal{N}=4$ SYM theory: an all-order result

Cited by in corpus (2)

• Vacuum expectation value of twist fields
• A Young diagram expansion of the hexagonal Wilson loop (amplitude) in $\mathcal{N}=4$ SYM