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We study supersymmetric index of 4d $SU(N)$ $mathcal{N}=4$ super Yang-Mills theory on $S^1 times M_3$. We compute asymptotic behavior of the index in the limit of shrinking $S^1$ for arbitrary $N$ by a refinement of supersymmetric Cardy formula. The asymptotic behavior for the superconformal index case ($M_3 =S^3$) at large $N$ agrees with the Bekenstein-Hawking entropy of rotating electrically charged BPS black hole in $AdS_5$ via a Legendre transformation as recently shown in literature. We also find that the agreement formally persists for finite $N$ if we slightly modify the AdS/CFT dictionary between Newton constant and $N$. This implies an existence of non-renormalization property of the quantum black hole entropy. We also study the cases with other gauge groups and additional matters, and the orbifold $mathcal{N}=4$ super Yang-Mills theory. It turns out that the entropies of all the CFT examples in this paper are given by $2pi sqrt{Q_1 Q_2 +Q_1 Q_3 +Q_2 Q_3 -2c(J_1 +J_2 )} $ with charges $Q_{1,2,3}$, angular momenta $J_{1,2}$ and central charge $c$. The results for other $M_3$ make predictions to the gravity side.
We reconsider warped black hole solutions in topologically massive gravity and find novel boundary conditions that allow for soft hairy excitations on the horizon. To compute the associated symmetry algebra we develop a general framework to compute a
We derive the general anomaly polynomial for a class of two-dimensional CFTs arising as twisted compactifications of a higher-dimensional theory on compact manifolds $mathcal{M}_d$, including the contribution of the isometries of $mathcal{M}_d$. We t
We discuss the connection between different entropies introduced for black hole. It is demonstrated on the two-dimensional example that the (quantum) thermodynamical entropy of a hole coincides (including UV-finite terms) with its statistical-mechani
One of the problems in the current asymptotic symmetry would be to extend the black hole to the rotating one. Therefore, in this paper, we obtain a four-dimensional asymptotically flat rotating black hole solution including the supertraslation corrections.
When two objects have gravitational interaction between them, they are no longer independent of each other. In fact, there exists gravitational correlation between these two objects. Inspired by E. Verlindes paper, we first calculate the entropy chan