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Register a new userCorrelation Functions and Hidden Conformal Symmetry of Kerr Black Holes
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Extremal scalar three-point correlators in the near-NHEK geometry of Kerr black holes have recently been shown to agree with the result expected from a holographically dual non-chiral two-dimensional conformal field theory. In this paper we extend this calculation to extremal three-point functions of scalars in a general Kerr black hole which need not obey the extremality condition $M=sqrt{J}$. It was recently argued that for low frequency scalars in the Kerr geometry there is a dual conformal field theory description which determines the interactions in this regime. Our results support this conjecture. Furthermore, we formulate a recipe for calculating finite-temperature retarded three-point correlation functions which is applicable to a large class of (even non-extremal) correlators, and discuss the vanishing of the extremal couplings.
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Dynamics in the throat of rapidly rotating Kerr black holes is governed by an emergent near-horizon conformal symmetry. The throat contains unstable circular orbits at radii extending from the ISCO down to the light ring. We show that they are related by conformal transformations to physical plunges and osculating trajectories. These orbits have angular momentum arbitrarily higher than that of ISCO. Using the conformal symmetry we compute analytically the radiation produced by the physical orbits. We also present a simple formula for the full self-force on such trajectories in terms of the self-force on circular orbits.
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We formulate two-dimensional rational conformal field theory as a natural generalization of two-dimensional lattice topological field theory. To this end we lift various structures from complex vector spaces to modular tensor categories. The central ingredient is a special Frobenius algebra object A in the modular category that encodes the Moore-Seiberg data of the underlying chiral CFT. Just like for lattice TFTs, this algebra is itself not an observable quantity. Rather, Morita equivalent algebras give rise to equivalent theories. Morita equivalence also allows for a simple understanding of T-duality. We present a construction of correlators, based on a triangulation of the world sheet, that generalizes the one in lattice TFTs. These correlators are modular invariant and satisfy factorization rules. The construction works for arbitrary orientable world sheets, in particular for surfaces with boundary. Boundary conditions correspond to representations of the algebra A. The partition functions on the torus and on the annulus provide modular invariants and NIM-reps of the fusion rules, respectively.
The most general operator product expansion in conformal field theory is obtained using the embedding space formalism and a new uplift for general quasi-primary operators. The uplift introduced here, based on quasi-primary operators with spinor indices only and standard projection operators, allows a unified treatment of all quasi-primary operators irrespective of their Lorentz group irreducible representations. This unified treatment works at the level of the operator product expansion and hence applies to all correlation functions. A very useful differential operator appearing in the operator product expansion is established and its action on appropriate products of embedding space coordinates is explicitly computed. This computation leads to tensorial generalizations of the usual Exton function for all correlation functions. Several important identities and contiguous relations are also demonstrated for these new tensorial functions. From the operator product expansion all correlation functions for all quasi-primary operators, irrespective of their Lorentz group irreducible representations, can be computed recursively in a systematic way. The resulting answer can be expressed in terms of tensor structures that carry all the Lorentz group information and linear combinations of the new tensorial functions. Finally, a summary of the well-defined rules allowing the computation of all correlation functions constructively is presented.
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