Universality of pseudoentropy for deformed spheres in dS/CFT

TL;DR

This paper investigates the universal behavior of pseudoentropy under small shape deformations of spheres in dS/CFT, revealing a universal quadratic correction linked to the stress-energy tensor correlator and extending known formulas to de Sitter holography.

Contribution

It demonstrates the universality of pseudoentropy corrections for deformed spheres in dS/CFT and extends the Mezei formula to this setting, applicable to non-unitary holographic CFTs.

Findings

Quadratic correction controlled by $C_T$ correlator.

Sphere remains a local extremum of pseudoentropy.

Universal behavior persists in higher-curvature gravity theories.

Abstract

We determine the universal part of pseudoentropy for small shape deformations of spherical entangling surfaces in the context of de Sitter/conformal field theory (dS/CFT) correspondence. The leading correction at quadratic order in the deformation parameter is controlled by the coefficient of the two-point stress-energy tensor correlator, $C_T$, of the non-unitary dual CFT, and it retains the sign of the unperturbed result, thereby establishing the sphere as a local extremum. The same structure holds in higher-curvature theories, as we check explicitly for quadratic curvature gravity, suggesting a universal behavior across non-unitary holographic CFTs. Our findings extend the Mezei formula to the dS/CFT setting and indicate that the shape dependence of pseudoentropy in dS holography resembles that of entanglement entropy in AdS space.