Renormalized pseudoentropy in dS/CFT

TL;DR

This paper develops a holographic framework for calculating finite pseudoentropy in non-unitary CFTs within dS/CFT, revealing universal contributions linked to the complex central charge and extending known formulas from AdS/CFT.

Contribution

It introduces a regulator-independent holographic pseudoentropy definition using conformal gravity and extends the Mezei formula to de Sitter space for small shape deformations.

Findings

Finite pseudoentropy is proportional to the complex central charge a*.

The formalism applies to spherical and deformed entangling surfaces.

An analytic continuation of the Mezei formula is obtained for dS/CFT.

Abstract

We study holographic pseudoentropy for subregions in non-unitary Euclidean conformal field theories (CFTs) within the framework of the de Sitter/conformal field theory (dS/CFT) correspondence. Pseudoentropy, defined as the von Neumann entropy of a transition matrix, is computed holographically from codimension-two extremal surfaces in dS space and is divergent due to the asymptotic bulk volume at future infinity. We show that a finite and regulator-independent definition follows from the on-shell action of conformal gravity in four and six dimensions, implemented through the replica construction. We illustrate the formalism for spherical entangling surfaces and small shape deformations thereof. The renormalized pseudoentropy isolates the universal contribution, which for a spherical entangling surface is proportional to the complex-valued central charge $a^\star$ of the non-unitary CFT. On an equal footing, for infinitesimal deformations away from the sphere, we recover, at quadratic order in the deformation parameter, an analytic continuation of the Mezei-like formula in its anti-de Sitter counterpart.