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

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 $θ< 0$ 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 $0<θ<d$, 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 $θ$ we find that new logarithmic contributions show up in the HEE formula for any $n$th-order gravity when $θ=d(d-1)/(d-2(n-1))$ and $d<2(n-1)$. In the range $0\leq θ<d$ we do not find additional logarithmic contributions appearing at any order except for $n=1$, which corresponds to the famous case $θ=d-1$ encountered in Einstein gravity.