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arXiv · 2306.06239

Protected and uniformly transcendental

Marco S. Bianchi
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Abstract

We show that the two-point function of protected bi-scalar operators in ${\cal N}=4$ SYM evaluated in dimensional regularization exhibits a uniform degree of transcendentality up to three-loop order. We conjecture that this property holds for the whole perturbative series and leverage the explicit results to postulate a prediction for the leading, order $\epsilon$, correction to all loop orders. We also consider the soft limit of three-point functions of such operators in momentum space and point out a simple and surprising perturbative relation to two-point functions, which we also extrapolate to all loop orders.

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Marco S. Bianchi. 2023-06-09. Protected and uniformly transcendental. https://arxiv.org/abs/2306.06239

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