The entropic $g$-theorem in general spacetime dimension

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