We consider the theory of gravitational quasi-normal modes for general linear perturbations of AdS4 black holes. Special emphasis is placed on the effective Schrodinger problems for axial and polar perturbations that realize supersymmetric partner potential barriers on the half-line. Using the holographic renormalization method, we compute the energy-momentum tensor for perturbations satisfying arbitrary boundary conditions at spatial infinity and discuss some aspects of the problem in the hydrodynamic representation. It is also observed in this general framework that the energy-momentum tensor of black hole perturbations and the energy momentum tensor of the gravitational Chern-Simons action (known as Cotton tensor) exhibit an axial-polar duality with respect to appropriately chosen supersymmetric partner boundary conditions on the effective Schrodinger wave-functions. This correspondence applies to perturbations of very large AdS4 black holes with shear viscosity to entropy density ratio equal to 1/4π, thus providing a dual graviton description of their hydrodynamic modes. We also entertain the idea that the purely dissipative modes of black hole hydrodynamics may admit Ricci flow description in the non-linear regime.
Carroll-Cotton Tensors and Gravitational Radiation at Null Infinity
École polytechnique, Centre National de la Recherche Scientifique – Unité Mixte de Recherche 7644, Institut Polytechnique de Paris（巴黎综合理工学院，法国国家科学研究中心联合研究单位7644，巴黎理工学院）；Université Libre de Bruxelles and International Solvay Institutes（布鲁塞尔自由大学和国际索尔维研究所）；International School for Advanced Studies (SISSA)（高级国际研究学院（SISSA））；Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Trieste（意大利国家核物理研究所的里雅斯特分部）；Université de Mons（蒙斯大学）
In three spacetime dimensions, (super)conformal geometry is controlled by the (super) Cotton tensor. We present a new duality transformation for N-extended supersymmetric theories formulated in terms of the linearised super-Cotton tensor or its higher spin extensions for the cases N=2, 1, 0. In the N=2 case, this transformation is a generalisation of the linear-chiral duality, which is known to provide a dual description in terms of chiral superfields for general models of self-interacting N=2 vector multiplets in three dimensions and N=1 tensor multiplets in four dimensions. For superspin-1 (…
We elaborate on the spin projection operators in three dimensions and use them to derive a new representation for the linearised higher-spin Cotton tensors.
We discuss conserved currents constructed from the Cotton tensor and (conformal) Killing-Yano tensors (KYTs). We consider the corresponding charges generally and then exemplify with the four-dimensional Plebański-Demiański metric where they are proportional to the sum of the squares of the electric and the magnetic charges. As part of the derivation, we also find the two conformal Killing-Yano tensors of the Plebański-Demiański metric in the recently introduced coordinates of Podolsky and Vratny. The construction of asymptotic charges for the Cotton current is elucidated and compared to the th…
In a conformally flat three-dimensional spacetime, the linearised higher-spin Cotton tensor $\mathfrak{C}_{α(n)}(h)$ is the unique conserved conformal current which is a gauge-invariant descendant of the conformal gauge prepotential $h_{α(n)}$. The explicit form of $\mathfrak{C}_{α(n)}(h)$ is well known in Minkowski space. Here we solve the problem of extending the Minkowskian result to the case of anti-de Sitter (AdS) space and derive a closed-form expression for $\mathfrak{C}_{α(n)}(h)$ in terms of the AdS Lorentz covariant derivatives. It is shown that every conformal higher-spin action $S_…
A first-order differential equation is provided for a one-form, spin-s connection valued in the two-row, width-(s-1) Young tableau of GL(5). The connection is glued to a zero-form identified with the spin-s Cotton tensor. The usual zero-Cotton equation for a symmetric, conformal spin-s tensor gauge field in 3D is the flatness condition for the sum of the GL(5) spin-s and background connections. This presentation of the equations allows to reformulate in a compact way the cohomological problem studied in 1511.07389, featuring the spin-s Schouten tensor. We provide full computational details for…
Using the asymptotic form of the bulk Weyl tensor, we present an explicit approach that allows us to reconstruct exact four-dimensional Einstein spacetimes which are algebraically special with respect to Petrov's classification. If the boundary metric supports a traceless, symmetric and conserved complex rank-two tensor, which is related to the boundary Cotton and energy-momentum tensors, and if the hydrodynamic congruence is shearless, then the bulk metric is exactly resummed and captures modes that stand beyond the hydrodynamic derivative expansion. We illustrate the method when the congruen…
In this paper we propose a space-time random tensor network approach for understanding holographic duality. Using tensor networks with random link projections, we define boundary theories with interesting holographic properties, such as the Renyi entropies satisfying the covariant Hubeny-Rangamani-Takayanagi formula, and operator correspondence with local reconstruction properties. We also investigate the unitarity of boundary theory in spacetime geometries with Lorenzian signature. Compared with the spatial random tensor networks, the space-time generalization does not require a particular ti…
We deal with the duality symmetry of the Dilaton field in cosmology and specifically with the so-called Gasperini-Veneziano duality transformation. In particular, we determine two conformal equivalent theories to the Dilaton field, and we show that under conformal transformations Gasperini-Veneziano duality symmetry does not survive. Moreover, we show that those theories share a common conservation law, of Noetherian kind, while the symmetry vector which generates the conservation law is an isometry only for the Dilaton field. Finally, we show that the Lagrangian of the Dilaton field is equiva…
The gauge theories underlying gauged supergravity and exceptional field theory are based on tensor hierarchies: generalizations of Yang-Mills theory utilizing algebraic structures that generalize Lie algebras and, as a consequence, require higher-form gauge fields. Recently, we proposed that the algebraic structure allowing for consistent tensor hierarchies is axiomatized by `infinity-enhanced Leibniz algebras' defined on graded vector spaces generalizing Leibniz algebras. It was subsequently shown that, upon appending additional vector spaces, this structure can be reinterpreted as a differen…
Given the Hamiltonian realisation of a topological (3+1)d gauge theory with finite group $G$, we consider a family of tensor network representations of its ground state subspace. This family is indexed by gapped boundary conditions encoded into module 2-categories over the input spherical fusion 2-category. Individual tensors are characterised by symmetry conditions with respect to non-local operators acting on entanglement degrees of freedom. In the case of Dirichlet and Neumann boundary conditions, we show that the symmetry operators form the fusion 2-categories $\mathsf{2Vec}_G$ of $G$-grad…
