Phys. Rev. D 99, 066014 (2019)

Holographic studies of the generic massless cubic gravities

Yue-Zhou Li^*

* Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University, Tianjin 300350, China

* liyuezhou@tju.edu.cn

ABSTRACT

‍We consider the generic massless cubic gravities coupled to a negative bare cosmological constant mainly in $D=5$ and $D=4$ dimensions, which are Einstein gravity extended with cubic curvature invariants where the linearized excited spectrum around the AdS background contains no massive modes. The generic massless cubic gravities are more general than Myers quasitopological gravity in $D=5$ and Einsteinian cubic gravity in $D=4$. It turns out that the massless cubic gravities admit the black holes at least in a perturbative sense with the coupling constants of the cubic terms becoming infinitesimal. The first order approximate black hole solutions with arbitrary boundary topology $k$ are presented, and in addition, the second order approximate planar black holes are exhibited as well. We then establish the holographic dictionary for such theories by presenting $a$-charge, $C_T$-charge and energy flux parameters $t_2$ and $t_4$. By perturbatively discussing the holographic Rényi entropy, we find $a$, $C_T$ and $t_4$ can somehow determine the Rényi entropy with the limit $q\to 1$, $q\to 0$ and $q\to \infty$ up to the first order, where $q$ is the order of the Rényi entropy. For holographic hydrodynamics, we discuss the shear-viscosity-entropy ratio and find that the patterns deviating from the Kovtun-Son-Starinets bound $1/\left(4\pi \right)$ can somehow be controlled by ($(c-a)/c,t_4$) up to the first order in $D=5$, and ($(C_T-\tilde{a})/C_T,t_4$) up to the second order in $D=4$, where $C_T$ and $\tilde{a}$ differ from $C_T$-charge and $a$-charge by inessential overall constants.