Holographic RG flows, entanglement entropy and the sum rule

TL;DR

This paper explores holographic RG flows, linking stress tensor correlators to central charge changes and entanglement entropy, while establishing stability and unitarity conditions in the dual gravity framework.

Contribution

It provides a holographic derivation of the sum rule relating stress tensor correlators to central charge and entanglement entropy, and proves reflection positivity via bulk stability.

Findings

The momentum squared term in the correlator encodes the change in central charge.

Holographic regularization matches finite and divergent sum rule terms.

Reflection positivity is proven through dual bulk action stability.

Abstract

We calculate the two-point function of the trace of the stress tensor in holographic renormalization group flows between pairs of conformal field theories. We show that the term proportional to the momentum squared in this correlator gives the change of the central charge between fixed points in d=2 and 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 for the renormalization of Newton's constant. Holographic regularization is found to 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 mutual information. Finally, we provide a general proof of reflection positivity in terms of stability of the dual bulk action, and discuss the relation between unitarity constraints, the null energy condition and regularity in the interior of the gravity solution.