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RG flows on two-dimensional spherical defects

Tom Shachar, Ritam Sinha, Michael Smolkin

SciPost Phys. 15, 240 (2023) · published 14 December 2023


We study two-dimensional spherical defects in d-dimensional Conformal Field Theories. We argue that the Renormalization Group (RG) flows on such defects admit the existence of a decreasing entropy function. At the fixed points of the flow, the entropy function equals the anomaly coefficient which multiplies the Euler density in the defect's Weyl anomaly. Our construction demonstrates an alternative derivation of the irreversibility of RG flows on two-dimensional defects. Moreover, in the case of perturbative RG flows induced by weakly relevant deformations, the entropy function decreases monotonically and plays the role of a C-function. We provide a simple example to explicitly work out the RG flow details in the proposed construction.

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Conformal field theory (CFT) Renormalization group (RG) Weyl anomalies

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