Real-time Correlators and Hidden Conformal Symmetry in Kerr/CFT Correspondence

In this paper, we study the real-time correlators in Kerr/CFT, in the low frequency limit of generic non-extremal Kerr(-Newman) black holes. From the low frequency scattering of Kerr-Newman black holes, we show that for the uncharged scalar scattering, there exists hidden conformal symmetry on the solution space. Similar to Kerr case, this suggests that the Kerr-Newman black hole is dual to a two-dimensional CFT with central charges $c_L=c_R=12J$ and temperatures $T_L=\frac{(r_++r_-)-Q^2/M}{4\pi a}, T_R=\frac{r_+-r_-}{4\pi a}$. Using the Minkowski prescription, we compute the real-time correlators of charged scalar and find perfect match with CFT prediction. We further discuss the low-frequency scattering of photons and gravitons by Kerr black hole and find that their retarded Green's functions are in good agreement with CFT prediction. Our study supports the idea that the hidden conformal symmetry in the solution space is essential to Kerr/CFT correspondence.Comment: 15 pages, Latex; typos corrected, references updated; minor correction, published versio

R\'enyi Mutual Information for Free Scalar in Even Dimensions

We compute the R\'enyi mutual information of two disjoint spheres in free massless scalar theory in even dimensions higher than two. The spherical twist operator in a conformal field theory can be expanded into the sum of local primary operators and their descendants. We analyze the primary operators in the replicated scalar theory and find the ones of the fewest dimensions and spins. We study the one-point function of these operators in the conical geometry and obtain their expansion coefficients in the OPE of spherical twist operators. We show that the R\'enyi mutual information can be expressed in terms of the conformal partial waves. We compute explicitly the R\'enyi mutual information up to order $z^d$, where $z$ is the cross ratio and $d$ is the spacetime dimension.Comment: 29 pages; More discussion on the partition function of primary operators, the contribution from spin-1 operator has been correcte

Hidden Conformal Symmetry and Quasi-normal Modes

We provide an algebraic way to calculate the quasi-normal modes of a black hole, which possesses a hidden conformal symmetry. We construct an infinite tower of quasi-normal modes from the highest-weight mode, in a simple and elegant way. For the scalar, the hidden conformal symmetry manifest itself in the fact that the scalar Laplacian could be rewritten in terms of the $SL(2,R)$ quadratic Casimir. For the vector and the tensor, the hidden conformal symmetry acts on them through Lie derivatives. We show that for three-dimensional black holes, with appropriate combination of the components the radial equations of the vector and the tensor could be written in terms of the Lie-induced quadratic Casimir. This allows the algebraic construction of the quasi-normal modes feasible. Our results are in good agreement with the previous study.Comment: 23 pages; references added; typos corrected, more clarifications, published versio

Strong Subadditivity and Emergent Surface

In this paper, we introduce two bounds which we call the Upper Differential Entropy and the Lower Differential Entropy for an infinite family of intervals(strips) in quantum field theory. The two bounds are equal provided that the theory is translational invariant and the entanglement entropy varies smoothly with respect to the interval. When the theory has a holographic dual, strong subadditivity of entanglement entropy indicates that there is always an emergent surface whose gravitational entropy is exactly given by the bound.Comment: 18 pages, 8 figures, replace "residual entropy" to "differential entropy

Three-loop planar master integrals for heavy-to-light form factors

We calculate analytically the three-loop planar master integrals relevant for heavy-to-light form factors using the method of differential equations. After choosing a proper canonical basis, the boundary conditions are easy to be determined, and the solution of differential equations is greatly simplified. The results for seventy-one master integrals at general kinematics are all expressed in terms of harmonic polylogarithms.Comment: 18 pages, 2 figure

Two-loop QCD Corrections to BcB_c Meson Leptonic Decays

The two-loop QCD radiative corrections to the $B_c$ meson leptonic decay rate are calculated in the framework of NRQCD factorization formalism. Two types of master integrals appearing in the calculation are obtained analytically for the first time. We get the short-distance coefficient of the leading matrix element to order $\alpha_s^2$ by matching the full perturbative QCD calculation results to the corresponding NRQCD ones. The result in this work helps the evaluation of the $B_c$ leptonic decay constant, as well as the Cabibbo-Kobayashi-Maskawa matrix element $|V_{cb}|$, to the full next-to-next-to-leading order degree of accuracy.Comment: Typos are correcte

Conical Defects, Black Holes and Higher Spin (Super-)Symmetry

We study the (super-)symmetries of classical solutions in the higher spin (super-)gravity in AdS$_3$. We show that the symmetries of the solutions are encoded in the holonomy around the spatial circle. When the spatial holonomies of the solutions are trivial, they preserve maximal symmetries of the theory, and are actually the smooth conical defects. We find all the smooth conical defects in the $sl(N), so(2N+1),sp(2N), so(2N), g_2$, as well as in $sl(N|N-1)$ and $osp(2N+1|2N)$ Chern-Simons gravity theories. In the bosonic higher spin cases, there are one-to-one correspondences between the smooth conical defects and the highest weight representations of Lie group. Furthermore we investigate the higher spin black holes in $osp(3|2)$ and $sl(3|2)$ higher spin (super-)gravity and find that they are only partially symmetric. In general, the black holes break all the supersymmetries, but in some cases they preserve part of the supersymmetries.Comment: 48 pages; more clarifications on conical defects in supersymmetric cas