We establish the irreversibility of renormalization group flows on a pointlike defect inserted in a $d$-dimensional Lorentzian conformal field theory. We identify the impurity entropy $g$ with the quantum relative entropy in two equivalent ways. One involves a null deformation of the Cauchy surface, and the other is given in terms of a local quench protocol. Positivity and monotonicity of the relative entropy imply that $g$ decreases monotonically along renormalization group flows, and provides a clear information-theoretic meaning for this irreversibility.

• Received 29 December 2022
• Accepted 1 March 2023

DOI:https://doi.org/10.1103/PhysRevLett.130.111603

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Published by the American Physical Society