Surface Defect, Anomalies and $b$-Extremization

Abstract

Quantum field theories (QFT) in the presence of defects exhibit new types of anomalies which play an important role in constraining the defect dynamics and defect renormalization group (RG) flows. Here we study surface defects and their anomalies in conformal field theories (CFT) of general spacetime dimensions. When the defect is conformal, it is characterized by a conformal $b$-anomaly analogous to the $c$-anomaly of 2d CFTs. The $b$-theorem states that $b$ must monotonically decrease under defect RG flows and was proven by coupling to a spurious defect dilaton. We revisit the proof by deriving explicitly the dilaton effective action for defect RG flow in the free scalar theory. For conformal surface defects preserving $\mathcal{N}=(0,2)$ supersymmetry, we prove a universal relation between the $b$-anomaly and the 't Hooft anomaly for the $U(1{)}_r$ symmetry. We also establish the $b$-extremization principle that identifies the superconformal $U(1{)}_r$ symmetry from $\mathcal{N}=(0,2)$ preserving RG flows. Together they provide a powerful tool to extract the $b$-anomaly of strongly coupled surface defects. To illustrate our method, we determine the $b$-anomalies for a number of surface defects in 3d, 4d and 6d SCFTs. We also comment on manifestations of these defect conformal and 't Hooft anomalies in defect correlation functions.

41 pages, 2 tables

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Cited by in corpus (13)

• Renormalization Group Flows on Line Defects
• Broken global symmetries and defect conformal manifolds
• Defect $a$-Theorem and $a$-Maximization
• Weyl Anomalies of Four Dimensional Conformal Boundaries and Defects
• The entropic $g$-theorem in general spacetime dimension
• RG flows on two-dimensional spherical defects
• Observations on BPS observables in 6d
• M2-doughnuts
• Ironing out the crease
• BPS surface operators and calibrations
• Information metric on the boundary
• EFT of 6D SUSY RG Flows
• The quantum UV-IR map for line defects in $\mathfrak{gl}(3)$-type class $S$ theories