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

Understand

The generalized Wilson loop operator interpolating between the supersymmetric and the ordinary Wilson loop in ${\cal N}=4$ SYM theory provides an interesting example of renormalization group flow on a line defect: the scalar coupling parameter $\zeta$ has 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 rank $k$ symmetric representation of $SU(N)$, we also consider a certain semiclassical limit where $k$ is taken to infinity with the product $k\, \zeta^2$ fixed.
• This limit can be conveniently studied using a 1d defect QFT representation in terms of $N$ commuting bosons.