Circular loop operators in conformal field theories

Abstract

We use the conformal group to study non-local operators in conformal field theories. A plane or a sphere (of any dimension) is mapped to itself by some subgroup of the conformal group, hence operators confined to that submanifold may be classified in representations of this subgroup. For local operators this gives the usual definition of conformal dimension and spin, but some conformal field theories contain interesting nonlocal operators, like Wilson or 't Hooft loops. We apply those ideas to Wilson loops in four-dimensional CFTs and show how they can be chosen to be in fixed representations of SL(2,R) x SO(3).

10 pages, latex

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Cited by in corpus (8)

• Small deformations of supersymmetric Wilson loops and open spin-chains
• Holographic drag force in 5d Kerr-AdS black hole
• Correlation function of circular Wilson loop with two local operators and conformal invariance
• Giant Wilson Loops and AdS${}_2$/dCFT${}_1$
• Boundary condition for D-brane from Wilson loop, and gravitational interpretation of eigenvalue in matrix model in AdS/CFT correspondence
• Classifying Superconformal Defects in Diverse Dimensions Part I: Superconformal Lines
• On strong-coupling correlation functions of circular Wilson loops and local operators
• Conformal line defects at finite temperature