TY - JOUR

T1 - Wilson loop in general representation and RG flow in 1D defect QFT

AU - Beccaria, M.

AU - Giombi, S.

AU - Tseytlin, A. A.

N1 - Funding Information:
We are grateful to S Komatsu and G Korchemsky for useful discussions. MB was supported by the INFN grant GSS (Gauge Theories, Strings and Supergravity). The work of SG is supported in part by the US NSF under Grant No. PHY-1914860. AAT was supported by the STFC Grant ST/T000791/1. Part of this work was done while AAT was a participant of the program ‘Confinement, Flux Tubes, and Large N’ at the KITP in Santa Barbara where his work was supported in part by the NSF under Grant No. PHY-1748958.
Publisher Copyright:
© 2022 The Author(s). Published by IOP Publishing Ltd.

PY - 2022/6/24

Y1 - 2022/6/24

N2 - 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 ζ 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 kζ 2 fixed. This limit can be conveniently studied using a 1D defect QFT representation in terms of N commuting bosons. Using this representation, we compute the beta function and the 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.

AB - 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 ζ 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 kζ 2 fixed. This limit can be conveniently studied using a 1D defect QFT representation in terms of N commuting bosons. Using this representation, we compute the beta function and the 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.

KW - conformal field theory

KW - defects in quantum field theory

KW - renormalization group flow

KW - supersymmetry

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U2 - 10.1088/1751-8121/ac7018

DO - 10.1088/1751-8121/ac7018

M3 - Article

AN - SCOPUS:85132397199

SN - 1751-8113

VL - 55

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

IS - 25

M1 - 255401

ER -