Viscosity Bound, Causality Violation and Instability with Stringy Correction and Charge

TL;DR

The paper investigates how stringy higher-derivative corrections (Gauss-Bonnet term) and electric charge influence the shear viscosity to entropy density ratio, causality, and stability in a holographic dual described by a charged RN-AdS black brane. Using a Kubo-formula approach for tensor perturbations, it derives $η/s=\frac{1}{4π}\left(1-4λ\left(1-\frac{a}{2}\right)\right)$, showing bound violation can persist with charge, while extremality restores the universal value. It then analyzes causality via the graviton effective speed $c_g^2(u)$ and finds a causality bound $λ\le 0.09$ (independent of $a$), with microcausality violation for larger $λ$ that charge cannot cure. Finally, it demonstrates an instability at large momentum due to the interplay of charge and GB terms, locating a critical line $λ_c(a)$ and showing that stability requires $λ\le 1/24$; a phase diagram maps the regions of viability. Overall, the work constrains admissible higher-derivative corrections at finite density and clarifies the conditions under which the holographic viscosity bound, causality, and stability coexist.

Abstract

Recently, it has been shown that if we consider the higher derivative correction, the viscosity bound conjectured to be $η/s=1/4π$ is violated and so is the causality. In this paper, we consider medium effect and the higher derivative correction simultaneously by adding charge and Gauss-Bonnet terms. We find that the viscosity bound violation is not changed by the charge. However, we find that two effects together create another instability for large momentum regime. We argue the presence of tachyonic modes and show it numerically. The stability of the black brane requires the Gauss-Bonnet coupling constant $λ$($=2α'/l^2$) to be smaller than 1/24. We draw a phase diagram relevant to the instability in charge-coupling space.

Figures (6)

• Figure 1: Shear viscosity to entropy density ratio as a function of $a$ and $\lambda$. The lines correspond to $\eta/s=0.07, 0.06,...,0.01$, respectively, from top to bottom.
• Figure 2: The hump (I) signifies the causality violation, while the well (II) indicates that the black brane is unstable.
• Figure 3: Schrödinger potential $V(r)$ as a function of $r$ for $\lambda=0.2$, $a=1.7$ and $k=500$. Near the horizon, the potential develops a negative-valued well and then negative-energy bound states will appear. Near the boundary, the potential develops a hump which corresponds to superluminal propagation of metastable quasiparticles.
• Figure 4: Phase diagram for the instability in $a$-$\lambda$ space. Region I: There are no causality violation and bulk bound states. Region II: Causality violation can happen, but bound states do not appear in the bulk. Region III: Both causality violation and instability happen in this region. Region IV: There is no causality violation, but the black brane is unstable.
• Figure 5: $c^2_g$ as a function of $u$. Line I describes the behavior of $c^2_g$ in region I for $\lambda=0.05$, $a=0.2$. Line II shows that $c^2_g>1$ at some value of $u$ near the boundary for $\lambda=0.14$, $a=0.4$.