Abstract:We construct the quartic version of generalized quasi-topological gravity, which was recently constructed to cubic order in arXiv:1703.01631. This class of theories includes Lovelock gravity and a known form of quartic quasi-topological gravity as special cases and possess a number of remarkable properties: (i) In vacuum, or in the presence of suitable matter, there is a single independent field equation which is a total derivative.(ii) At the linearized level, the equations of motion on a maximally symmetric background are second order, coinciding with the linearized Einstein equations up to a redefinition of Newton's constant. Therefore, these theories propagate only the massless, transverse graviton on a maximally symmetric background. (iii) While the Lovelock and quasi-topological terms are trivial in four dimensions, there exist four new generalized quasi-topological terms (the quartet) that are nontrivial, leading to interesting higher curvature theories in d ≥ 4 dimensions that appear well suited for holographic study. We construct four dimensional black hole solutions to the theory and study their properties. A study of black brane solutions in arbitrary dimensions reveals that these solutions are modified from the 'universal' properties they possess in other higher curvature theories, which may lead to interesting consequences for the dual CFTs.

We investigate the thermodynamics of AdS black holes in Generalized Quasitopological Gravity with and without electric charge, concentrating on the version of the theory that is cubic in curvature. We study new aspects of Hawking-Page transitions that occur for these black holes. Working within the framework of black hole chemistry, we find a variety of familiar and new critical behaviour and phase transitions in four and higher dimensions for the charged black holes. We also consider some holographic aspects of our work, demonstrating how the ratio of viscosity to entropy is modified by inclusion of these cubic curvature terms.

Using the compatibility of the anomalous Chern-Simons couplings on D p -branes with the linear T-duality and with the antisymmetric B-field gauge transformations, some couplings have been recently found for C (p−3) at order O(α ′2 ). We examine these couplings with the S-matrix element of one RR and two antisymmetric B-field vertex operators. We find that the S-matrix element reproduces these couplings as well as some other couplings. Each of them is invariant under the linear T-duality and the B-field gauge transformations. 0

We investigate the thermodynamic behaviour of asymptotically anti de Sitter black holes in generalized quasi-topological gravity containing terms both cubic and quartic in the curvature. We investigate the general conditions required for physical phase transitions and critical behaviour in any dimension and then consider in detail specific properties in spacetime dimensions 4, 5, and 6. We find for spherical black holes that there are respectively at most two and three physical critical points in five and six dimensions. For hyperbolic black holes we find the occurrence of Van der Waals phase transitions in four dimensions and reverse Van der Waals phase transitions in dimensions greater than 4 if both cubic and quartic curvature terms are present. We also observe the occurrence of phase transitions in for fixed chemical potential. We consider some applications of our work in the dual CFT, investigating how the ratio of viscosity to entropy is modified by inclusion of these higher curvature terms. We conclude that the presence of the quartic curvature term results in a violation of the KSS bound in five dimensions, but not in other dimensions.

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Recently, it has been found that there are couplings of the RR field strength F (p) and the B-field strength H on the world volume of D p -branes at order O(α ′2 ). These couplings which have both world-volume and transverse indices, are invariant under the linear T-duality transformations. Consistency with the nonlinear T-duality indicates that the RR field strength F (p) in these couplings should be replaced by F (p) = dC (p−1) where C = e B C. This replacement, however, produces some nongauge invariant terms. On the other hand, the nonlinear terms are invariant under the linear T-duality transformations at the level of two B-fields. This allows one to remove some of the nonlinear terms in F (p) . We fix this by comparing the nonlinear couplings with the S-matrix element of one RR and two NSNS vertex operators. Our results indicate that in the expansion of F (p) one should keep only the B-field gauge invariant terms, e.g., B ∧ dC (p−3) where both indices of B-field lie along the brane. Moreover, in this case one should replace B with B + 2πα ′ f to have the B-field gauge invariance.0

We obtain a perturbative solution for rotating charged black holes in 5-dimensional Einstein-Maxwell-Chern-Simons theory with a negative cosmological constant. We start from a small undeformed Kerr-AdS solution and use the electric charge as a perturbative parameter to build up black holes with equal-magnitude angular momenta up to forth order. These black hole solutions are described by three parameters, the charge, horizon radius and horizon angular velocity. We determine the physical quantities of these black holes and study their dependence on the parameters of black holes and arbitrary Chern-Simons coefficient. In particular, for values of CS coupling constant beyond its supergravity amount, due to a rotational instability, counterrotating black holes arise. Also the rotating solutions appear to have vanishing angular momenta and do not manifest uniquely by their global charges.

We use the relation between certain diffeomorphisms in the bulk and Weyl transformations on the boundary to build the conformal structure of the metric in the presence of matter in the bulk. We explicitly obtain the conformal anomaly in any spacetime dimension d in a holographic frame work in the case of gravity coupled to the scalar fields. This way we also provide a holographic construction of the bulk spacetime metric and of the matter fields in the bulk of this spacetime out of sources that are related to conformal field theory data. With the latter, we produce an asymptotic expansion of the bulk fields and scalar fields near the boundary in terms of spacetime dimension in the context of the AdS/CFT correspondence. We work out both the gravitational and matter conformal anomalies of the boundary theory as a coefficient of the infrared logarithmic divergence that appears in the on-shell action.