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

Abstract: The generalized Wilson loop operator interpolating between the supersymmetric and the ordinary Wilson loop in 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. 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 away from 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 study a certain ``semiclassical'' limit where k is taken to infinity with k \zeta^2 fixed. This limit can be conveniently studied using a 1d defect QFT representation in terms of path integral over N commuting 1d bosons. Using this representation, we compute the beta function and circular loop expectation value in the large k limit, 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. based on joint work with Matteo Beccaria and Simone Giombi

HEP - theorymathematical physicsexactly solvable and integrable systems

Audience: researchers in the topic

London Integrability Journal Club

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