Holographic renormalization flows, entanglement entropy and the sum rule

CASINI, HORACIO; TESTE, EDUARDO; TORROBA, GONZALO

JOURNAL OF HIGH ENERGY PHYSICS - (Online)

SISSA

Año: 2016

1029-8479

We calculate the two-point function of the trace of the stress tensor inholographic renormalization group flows between pairs of conformal fieldtheories. We show that the term proportional to the momentum squared in thiscorrelator gives the change of the central charge between fixed points in d=2and in d>2 it gives the holographic entanglement entropy for a planar region.This can also be seen as a holographic realization of the Adler-Zee formula forthe renormalization of Newton´s constant. Holographic regularization is foundto provide a perfect match of the finite and divergent terms of the sum rule,and it is analogous to the regularization of the entropy in terms of mutualinformation. Finally, we provide a general proof of reflection positivity interms of stability of the dual bulk action, and discuss the relation betweenunitarity constraints, the null energy condition and regularity in the interiorof the gravity solution.