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Protected and uniformly transcendental
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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.
Forward citations
Cited by 2 Pith papers
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Bootstrapping form factor squared in ${\cal N}=4$ super-Yang-Mills
A bootstrap using soft and collinear limits fixes the tree-level form factor squared in planar N=4 SYM up to N=6, unifying loop integrands from two-point master diagrams.
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Correlators in non-conformal $\mathcal{N}=2$ gauge theories from localization
Two-point correlators of chiral/anti-chiral operators in SU(N) N=2 gauge theories with a non-zero beta function, computed by Feynman diagrams in flat space, match sphere-localization matrix model results exactly throu...
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