Area law of connected correlation function in higher dimensional conformal field theory

TL;DR

This paper establishes an area law for the correlator of OPE blocks in higher-dimensional conformal field theories, revealing parallels with black hole entropy and geometric entanglement entropy, including leading and subleading terms.

Contribution

It introduces a new area law for correlators in higher-dimensional CFTs, highlighting the structure of leading and logarithmic subleading terms and analyzing their coefficients.

Findings

The area law includes a leading term proportional to the entanglement surface area.

A logarithmic subleading term with degree q is identified.

UV cutoff independent coefficients are extracted and analyzed.

Abstract

We present a new area law which is associated with the correlator of OPE blocks in higher dimensional conformal field theories (CFTs). The area law shows similar behaviour as black hole entropy or geometric entanglement entropy. It includes a leading term which is proportional to the area of the entanglement surface, and a logarithmic subleading term with degree $q$. We extract the UV cutoff independent coefficients and discuss various properties of the coefficients.