Renormalization Group Flows on Line Defects

Abstract

We consider line defects in d-dimensional Conformal Field Theories (CFTs). The ambient CFT places nontrivial constraints on Renormalization Group (RG) flows on such line defects. We show that the flow on line defects is consequently irreversible and furthermore a canonical decreasing entropy function exists. This construction generalizes the g theorem to line defects in arbitrary dimensions. We demonstrate our results in a flow between Wilson loops in 4 dimensions.

5 pages, 1 figure v2 added ref.s v3 minor corrections v4 matches published version

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• The entropic $g$-theorem in general spacetime dimension
• Phases of Wilson Lines in Conformal Field Theories
• Wilson loop in general representation and RG flow in 1d defect QFT
• Line Operators in Chern-Simons-Matter Theories and Bosonization in Three Dimensions
• RG flows on two-dimensional spherical defects
• Defects in scalar field theories, RG flows and Dimensional Disentangling
• Universal Dynamics of Heavy Operators in Boundary CFT${}_2$
• Interpolating Wilson loops and enriched RG flows
• Large Charges on the Wilson Loop in $\mathcal{N}=4$ SYM: Matrix Model and Classical String
• Interacting conformal scalar in a wedge
• Line operators in Chern-Simons-Matter theories and Bosonization in Three Dimensions II -Perturbative Analysis and All-loop Resummation
• Method of images in defect conformal field theories
• Large Charges on the Wilson Loop in $\mathcal{N}=4$ SYM: II. Quantum Fluctuations, OPE, and Spectral Curve
• Defect Localized Entropy: Renormalization Group and Holography
• The quantum UV-IR map for line defects in $\mathfrak{gl}(3)$-type class $S$ theories
• A network of hyperloops