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arXiv · 1607.02084

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

Alfredo Bonini·Davide Fioravanti·Simone Piscaglia·Marco Rossi
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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.

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Alfredo Bonini, Davide Fioravanti, Simone Piscaglia, Marco Rossi. 2016-07-07. The contribution of scalars to ${\cal N}=4$ SYM amplitudes. https://doi.org/10.1103/physrevd.95.041902

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