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

Author(s): Beccaria, M; Giombi, Simone; Tseytlin, AA

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Abstract: <jats:title>Abstract</jats:title><jats:p>The generalized Wilson loop operator interpolating between the supersymmetric and the ordinary Wilson loop in<jats:inline-formula><jats:tex-math><?CDATA $\mathcal{N}=4$?></jats:tex-math><mml:math xmlns:mml="" display="inline" overflow="scroll"><mml:mi mathvariant="script">N</mml:mi><mml:mo>=</mml:mo><mml:mn>4</mml:mn></mml:math><jats:inline-graphic xmlns:xlink="" xlink:href="aac7018ieqn24.gif" xlink:type="simple" /></jats:inline-formula>SYM theory provides an interesting example of renormalization group flow on a line defect: the scalar coupling parameter<jats:italic>ζ</jats:italic>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<jats:italic>k</jats:italic>symmetric representation of<jats:italic>SU</jats:italic>(<jats:italic>N</jats:italic>), we also consider a certain ‘semiclassical’ limit where<jats:italic>k</jats:italic>is taken to infinity with the product<jats:italic>kζ</jats:italic><jats:sup>2</jats:sup>fixed. This limit can be conveniently studied using a 1D defect QFT representation in terms of<jats:italic>N</jats:italic>commuting bosons. Using this representation, we compute the beta function and the circular loop expectation value in the large<jats:italic>k</jats:italic>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.</jats:p>
Publication Date: 6-Jun-2022
Electronic Publication Date: 6-Jun-2022
Citation: Beccaria, M, Giombi, S, Tseytlin, AA. (2022). Wilson loop in general representation and RG flow in 1D defect QFT. Journal of Physics A: Mathematical and Theoretical, 55 (25), 255401 - 255401. doi:10.1088/1751-8121/ac7018
DOI: doi:10.1088/1751-8121/ac7018
ISSN: 1751-8113
EISSN: 1751-8121
Keywords: conformal field theory, supersymmetry, defects in quantum field theory, renormalization group flow
Pages: 255401 - 255401
Type of Material: Journal Article
Journal/Proceeding Title: Journal of Physics A: Mathematical and Theoretical
Version: Final published version. This is an open access article.

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