Higher Derivative Corrections to Holographic Entanglement Entropy for AdS Solitons

TL;DR

This work analyzes holographic entanglement entropy in AdS soliton backgrounds when higher derivative corrections are included, via ${ extR}^4$ terms in Type IIB and M-theory and Gauss-Bonnet gravity. It derives leading corrections to the HEE functional, showing that finite parts scale with the underlying gauge theory parameters (e.g., $N$, $oldsymbol{ extlambda}$) and, in the Gauss-Bonnet setting, examines how the confinement/deconfinement-like phase transition depends on the subsystem size and the GB coupling $oldsymbol{ exteta}$. Within the standard causality bounds for GB gravity, the qualitative phase structure remains similar to Einstein gravity, though outside these bounds pathologies such as non-smooth minimal surfaces or ill-defined entropies can arise. The results provide concrete quantitative corrections to HEE in string/M-theory and clarify the reliability of holographic entanglement calculations when higher derivative corrections are present, with implications for strongly coupled confining gauge theories.

Abstract

We investigate the behaviors of holographic entanglement entropy for AdS soliton geometries in the presence of higher derivative corrections. We calculate the leading higher derivative corrections for the AdS5 setup in type IIB string and for the AdS4,7 ones in M-theory. We also study the holographic entanglement entropy in Gauss-Bonnet gravity and study how the confinement/deconfinement phase transition observed in AdS solitons is affected by the higher derivative corrections.

Figures (7)

• Figure 1: The bounds for $g(r_s)\ge -1/2$\ref{['paramrestriction01']}\ref{['rc']} (red) on the $(r_s/r_0, \eta)$-plane. Lines for $\eta = 1/4, 9/100, -1/8, -7/36, -5/16$ are also displayed.
• Figure 2: Patterns of extremal curved surfaces $\gamma_A$ (projected on the $(r,x)$-plane). The integrand of \ref{['heeo']} is locally minimum on the red lines and maximum on the blue one. Therefore we only have to consider (a) and (b).
• Figure 3: Two patterns of "trivial" $\gamma_A$. They have different values of $S_A$ due to the boundary term $q(r_0)$, accounted only for (e). For $\eta < 0$, (e) is preferred to (d), and vice versa for $\eta > 0$.
• Figure 4: $(l,S_A)$ plots for variable $0 \le \eta \le {{1}/{4}}$. The unit for $l$ and $S_A$ are $R$ and ${{\pi V_yL}/{2G_N^{(5)}}}$, respectively. The value for the phase (d) is taken to be $0$ for $S_A$.
• Figure 5: $(l,S_A)$ plots for variable $\eta\le 0$. The value for the disconnected phase (e) is taken to be $0$ for $S_A$.