Wilson loop in general representation and RG flow in 1D defect QFT

Abstract

AbstractThe generalized Wilson loop operator interpolating between the supersymmetric and the ordinary Wilson loop inN=4SYM theory provides an interesting example of renormalization group flow on a line defect: the scalar coupling parameterζhas a non-trivial beta function and may be viewed as a running coupling constant in a 1D defect QFT. In this paper we continue the study of this operator, generalizing previous results for the beta function and Wilson loop expectation value to the case of an arbitrary representation of the gauge group and beyond the planar limit. Focusing on the scalar ladder limit where the generalized Wilson loop reduces to a purely scalar line operator in a free adjoint theory, and specializing to the case of the rankksymmetric representation ofSU(N), we also consider a certain ‘semiclassical’ limit wherekis taken to infinity with the productkζ2fixed. This limit can be conveniently studied using a 1D defect QFT representation in terms ofNcommuting bosons. Using this representation, we compute the beta function and the circular loop expectation value in the largeklimit, and use it to derive constraints on the structure of the beta function for general representation. We discuss the corresponding 1D RG flow and comment on the consistency of the results with the 1D defect version of the F-theorem.