  There appears a universal logarithmic term of entanglement entropy, i.e.,
$-a(\Omega) \log(H/\delta)$, for 3d CFTs when the entangling surface has a
sharp corner. $a(\Omega)$ is a function of the corner opening angle and behaves
as $a(\Omega\to \pi)\simeq \sigma (\pi-\Omega)^2$ and $a(\Omega\to 0)\simeq
\kappa/\Omega$, respectively. Recently, it is conjectured that
$\sigma/C_T=\pi^2/24 $, where $C_T$ is central charge in the stress tensor
correlator, is universal for general CFTs in three dimensions. In this paper,
by applying the general higher curvature gravity, we give a holographic proof
of this conjecture. We also clarify some interesting problems. Firstly, we find
that, in contrast to $\sigma/C_T$, $\kappa/C_T$ is not universal. Secondly, the
lower bound $a_E(\Omega)/C_T$ associated to Einstein gravity can be violated by
higher curvature gravity. Last but not least, we find that there are similar
universal laws for CFTs in higher dimensions. We give some holographic tests of
these new conjectures.
