Higher-curvature corrections to holographic entanglement entropy in geometries with hyperscaling violation

TL;DR

This paper investigates how higher-curvature corrections affect holographic entanglement entropy in geometries with hyperscaling violation, revealing new divergences and logarithmic terms depending on the parameters and gravity order.

Contribution

It provides a general conjecture for the HEE expression with higher-order gravity and analyzes the emergence of divergences and logarithmic terms in various parameter regimes.

Findings

New divergence for $ heta<0$ in curvature-squared gravities.

Logarithmic contributions for negative $ heta$ at specific parameter values.

No additional logarithmic terms for $0 \\leq \theta < d$ except in the Einstein case.

Abstract

We study the effects of including higher-curvature corrections to the Einstein gravity bulk action on the holographic entanglement entropy (HEE) expression for geometries with hyperscaling violation (hvLf). For $\theta< 0$ we show that one single new divergence arises for general curvature-squared gravities, which allows us to conjecture the general expression of HEE for any higher-order gravity action. For $0<\theta<d$, we assume the hvLf geometry to arise above some intermediate scale $r_F$, becoming AdS in the UV and perform a similar analysis for $R^n$ gravities. For negative values of $\theta$ we find that new logarithmic contributions show up in the HEE formula for any $n$th-order gravity when $\theta=d(d-1)/(d-2(n-1))$ and $d<2(n-1)$. In the range $0\leq \theta<d$ we do not find additional logarithmic contributions appearing at any order except for $n=1$, which corresponds to the famous case $\theta=d-1$ encountered in Einstein gravity.