Universality of pseudoentropy for deformed spheres in dS/CFT

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.

Figures (2)

• Figure 1: In green, the entangling region $\mathbb B^{d-1}_\epsilon$ is the perturbation around the unit-ball $\mathbb B^{d-1}$, stereographically projected on $\mathbb S^{d-1}$.
• Figure 2: (Left) Front view of the RT surface for small perturbations around the ball-shaped entangling region at future infinity. (Right) Top view of the same RT surface. The timelike section is shown in orange, while the spacelike part is highlighted in blue. The black line indicates the junction at $\tau = \tau_E = 0$. The sketch is not conformal; therefore, the upper part does not correspond to future infinity, but to some value of $0<\tau<\infty$.