A Modified Cosmic Brane Proposal for Holographic Renyi Entropy

TL;DR

This paper introduces a new formula for holographic Renyi entropies that extends the cosmic brane proposal, especially predicting new phase corrections for Renyi index less than one, supported by illustrative examples and existing models.

Contribution

It proposes a modified holographic Renyi entropy formula based on fixed-area states, revealing new phase corrections for Renyi index below one and clarifying the optimization differences.

Findings

Agreement with cosmic brane proposal for n≥1

Prediction of new phase with corrections for n<1

Reproduction of known results in PSSY model and high-energy states

Abstract

We propose a new formula for computing holographic Renyi entropies in the presence of multiple extremal surfaces. Our proposal is based on computing the wave function in the basis of fixed-area states and assuming a diagonal approximation for the Renyi entropy. For Renyi index $n\geq1$, our proposal agrees with the existing cosmic brane proposal for holographic Renyi entropy. For $n<1$, however, our proposal predicts a new phase with leading order (in Newton's constant $G$) corrections to the cosmic brane proposal, even far from entanglement phase transitions and when bulk quantum corrections are unimportant. Recast in terms of optimization over fixed-area states, the difference between the two proposals can be understood to come from the order of optimization: for $n<1$, the cosmic brane proposal is a minimax prescription whereas our proposal is a maximin prescription. We demonstrate the presence of such leading order corrections using illustrative examples. In particular, our proposal reproduces existing results in the literature for the PSSY model and high-energy eigenstates, providing a universal explanation for previously found leading order corrections to the $n<1$ Renyi entropies.