A defect action for Wilson loops

Abstract

An effective action is proposed to compute the expectation value of Wilson loops in $(S)U(N)$ gauge theories. The action consists of fermions localized on the loop and an Abelian gauge field that fixes the representation. The discussion is limited to weak coupling and Wilson loops in the fundamental representation extended along a smooth curve, but there are no restrictions on the matter content as long as the theory has a UV fixed point or it is conformal. For a circular Wilson loop it is found that the expectation value coincides at leading order with the exact result of the $1/2$ BPS Wilson loop of $\mathcal{N}=4$ super Yang-Mills, which is determined by a solvable Gaussian matrix model. This hints towards a universal connection to string theory duals and SYK models.

19 pages + appendices, 2 figures, references added

References in corpus (6)

• Gluon scattering amplitudes at strong coupling
• Holographic Wilson Loops
• A limit for large $R$-charge correlators in $\mathcal{N}=2$ theories
• Non-supersymmetric Wilson loop in N=4 SYM and defect 1d CFT
• Strange metals and the AdS/CFT correspondence
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Cited by in corpus (9)

• Towards a $C$-theorem in defect CFT
• Correlators on non-supersymmetric Wilson line in N=4 SYM and AdS${}_2$/CFT${}_1$
• Wilson loop in general representation and RG flow in 1d defect QFT
• Spin chain integrability in non-supersymmetric Wilson loops
• Defect Localized Entropy: Renormalization Group and Holography
• Wilson loops in Large Symmetric Representations through a Double-Scaling Limit
• Wilson loops in $\mathcal{N}=4$ $SO(N)$ SYM and D-Branes in $Ad{S}_5\times {\mathbb{RP}}^5$
• Holographic RG flow and reparametrization invariance of Wilson Loops
• Higher order RG flow on the Wilson line in $\mathcal{N}=4$ SYM