The entropic $g$-theorem in general spacetime dimension

Understand

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.