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

TL;DR

This paper investigates how stringy corrections, charge, and higher derivative terms affect viscosity bounds, causality, and stability in black brane models, revealing that combined effects lead to new instabilities and phase transitions.

Contribution

It demonstrates that charge does not restore the viscosity bound violation caused by higher derivative corrections and identifies a new instability due to combined effects, establishing a stability criterion for the Gauss-Bonnet coupling.

Findings

Viscosity bound violation persists with charge.

Combined effects induce tachyonic instabilities at large momentum.

Stability requires Gauss-Bonnet coupling to be less than 1/24.

Abstract

Recently, it has been shown that if we consider the higher derivative correction, the viscosity bound conjectured to be $\eta/s=1/4\pi$ 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 $\lambda$($=2\alpha'/l^2$) to be smaller than 1/24. We draw a phase diagram relevant to the instability in charge-coupling space.