We study heavy-light four-point function by employing Lorentzian inversion formula, where the conformal dimension of heavy operator is as large as central charge C T → ∞. We implement the Lorentzian inversion formula back and forth to reveal the universality of the lowest-twist multi-stress-tensor T k as well as large spin double-twist operators [O H O L ] n ,J. In this way, we also propose an algorithm to bootstrap the heavylight four-point function by extracting relevant OPE coefficients and anomalous dimensions. By following the algorithm, we exhibit the explicit results in d = 4 up to the triple-stresstensor. Moreover, general dimensional heavy-light bootstrap up to the double-stress-tensor is also discussed, and we present an infinite series representation of the lowest-twist doublestress-tensor OPE coefficient. Exact expressions of lowest-twist double-stress-tensor OPE coefficients in d = 6, 8, 10 are also obtained as further examples.

We study the OPE coefficients c ∆,J for heavy-light scalar four-point functions, which can be obtained holographically from the two-point function of a light scalar of some non-integer conformal dimension ∆ L in an AdS black hole. We verify that the OPE coefficient c d,0 = 0 for pure gravity black holes, consistent with the tracelessness of the holographic energymomentum tensor. We then study the OPE coefficients from black holes involving matter fields. We first consider general charged AdS black holes and we give some explicit low-lying examples of the OPE coefficients. We also obtain the recursion formula for the lowest-twist OPE coefficients with at most two current operators. For integer ∆ L , although the OPE coefficients are not fully determined, we set up a framework to read off the coefficients γ ∆,J of the log(zz) terms that are associated with the anomalous dimensions of the exchange operators and obtain a general formula for γ ∆,J . We then consider charged AdS black holes in gauged supergravity STU models in D = 5 and D = 7, and their higher-dimensional generalizations. The scalar fields in the STU models are conformally massless, dual to light operators with ∆ L = d − 2. We derive the linear perturbation of such a scalar in the STU charged AdS black holes and obtain the explicit OPE coefficient c d−2,0 . Finally, we analyse the asymptotic properties of scalar hairy AdS black holes and show how c d,0 can be nonzero with exchanging scalar operators in these backgrounds.The AdS/CFT correspondence establishes an insightful routine to investigate a strongly coupled conformal field theory (CFT) by using appropriate weakly coupled gravity in antide Sitter (AdS) spacetime and vice versa [1]. Originally, the AdS/CFT correspondence is typically referred to as the duality between type IIB superstring in AdS 5 × S 5 and N = 4, d = 4 super Yang-Mills theory. The holographic principle is expected to be more general and can apply to a variety of gravity theories even without supersymmetry, and indeed it has passed a large amount of tests at the AdS scale, i.e. the locality holds at the scale that is never shorter than the AdS radius ℓ [2]. The results include the correct structures of two-point functions, three-point functions [3,4], conformal anomalies [5,6] in CFTs that are fixed by the virtue of conformal symmetry. Typically, even though the structures are the same, different gravity theories may lead to different CFT data. Thus gravities can be served as effective CFTs. By finding relations and bounds from the holographic CFT data that follow exactly the same pattern regardless of the specific details of a gravity theory, some universal properties of CFTs can be revealed. Known examples include the controlling pattern of shear-viscosity/entropy ratio and entanglement entropy by central charges [7-10], central charge relations [11-13].Below the AdS scale where the higher-point correlation functions (≥ 4) come out to be visible, the generality of AdS/CFT becomes highly nontrivial. Fortunately, it was argued that...

Quasi-topological terms in gravity can be viewed as those that give no contribution to the equations of motion for a special subclass of metric ansätze. They therefore play no rôle in constructing these solutions, but can affect the general perturbations. We consider Einstein gravity extended with Ricci tensor polynomial invariants, which admits Einstein metrics with appropriate effective cosmological constants as its vacuum solutions. We construct three types of quasi-topological gravities. The first type is for the most general static metrics with spherical, toroidal or hyperbolic isometries. The second type is for the special static metrics where g tt g rr is constant. The third type is the linearized quasi-topological gravities on the Einstein metrics. We construct and classify results that are either dependent on or independent of dimensions, up to the tenth order. We then consider a subset of these three types and obtain Lovelock-like quasi-topological gravities, that are independent of the dimensions. The linearized gravities on Einstein metrics on all dimensions are simply Einstein and hence ghost free. The theories become quasi-topological on static metrics in one specific dimension, but non-trivial in others. We also focus on the quasi-topological Ricci cubic invariant in four dimensions as a specific example to study its effect on holography, including shear viscosity, thermoelectric DC conductivities and butterfly velocity. In particular, we find that the holographic diffusivity bounds can be violated by the quasitopological terms, which can induce an extra massive mode that yields a butterfly velocity unbound above. †

In this paper, we study Einstein gravity extended with Ricci polynomials and derive the constraints on the coupling constants from the considerations of being ghost free, exhibiting an a-theorem and maintaining causality. The salient feature is that Einstein metrics with appropriate effective cosmological constants continue to be solutions with the inclusion of such Ricci polynomials and the causality constraint is automatically satisfied. The ghost free and a-theorem conditions can only be both met starting at the quartic order. We also study these constraints on general Riemann cubic gravities. †

We study the static equilibrium of a charged massive particle around a charged black hole, balanced by the Lorentz force. For a given black hole, the equilibrium surface is determined by the charge/mass ratio of the particle. By investigating a large class of charged black holes, we find that the equilibria can be stable, marginal or unstable. We focus on the unstable equilibria which signal chaotic motions and we obtain the corresponding Lyapunov exponents λ. We find that although λ approaches universally the horizon surface gravity κ when the equilibria are close to the horizon, the proposed chaotic motion bound λ < κ is satisfied only by some specific black holes including the RN and RN-AdS black holes. The bound can be violated by a large number of black holes including the RN-dS black holes or black holes in Einstein-Maxwell-Dilaton, Einstein-Born-Infeld and Einstein-Gauss-Bonnet-Maxwell gravities. We find that unstable equilibria can even exist in extremal black holes, implying that the ratio λ/κ can be arbitrarily large for sufficiently small κ. Our investigation does suggest a universal bound for sufficiently large κ, namely λ/κ < C for some order-one constant C. †