The entropic $g$-theorem in general spacetime dimension

Abstract

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.

v2: minor corrections, matches published version. 6 pages, 2 figures

References in corpus (4)

• Towards a derivation of holographic entanglement entropy
• The g-theorem and quantum information theory
• Irreversibility in quantum field theories with boundaries
• Boundary Entropy Can Increase Under Bulk RG Flow

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