Abstract
Extending earlier work, we find the two-loop term in the beta-function for the scalar coupling ζ in a generalized Wilson loop operator of the mathcal{N} = 4 SYM theory, working in the planar weak-coupling expansion. The beta-function for ζ has fixed points at ζ = ±1 and ζ = 0, corresponding respectively to the supersymmetric Wilson-Maldacena loop and to the standard Wilson loop without scalar coupling. As a consequence of our result for the beta-function, we obtain a prediction for the two-loop term in the anomalous dimension of the scalar field inserted on the standard Wilson loop. We also find a subset of higher-loop contributions (with highest powers of ζ at each order in ‘t Hooft coupling λ) coming from the scalar ladder graphs determining the corresponding terms in the five-loop beta-function. We discuss the related structure of the circular Wilson loop expectation value commenting, in particular, on consistency with a 1d defect version of the F-theorem. We also compute (to two loops in the planar ladder model approximation) the two-point correlators of scalars inserted on the Wilson line.
Highlights
In [10] and further studied in [11, 12]
Extending earlier work, we find the two-loop term in the beta-function for the scalar coupling ζ in a generalized Wilson loop operator of the N = 4 SYM theory, working in the planar weak-coupling expansion
As a consequence of our result for the beta-function, we obtain a prediction for the two-loop term in the anomalous dimension of the scalar field inserted on the standard Wilson loop
Summary
We shall present the derivation of the coefficients of the λnζ2n+1 terms in the beta-function (1.10). For a set of couplings ζi we have βi. Conformal point, i.e. if X(ζ∗) = 0
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