Partition functions of higher spin black holes and their CFT duals

By Per Kraus, Eric Perlmutter. 2011

213 citations recorded by the source corpus.

A bstractWe find black hole solutions of D = 3 higher-spin gravity in the hs[λ] ⊕ hs[λ] Chern-Simons formulation. These solutions have a spin-3 chemical potential, and carry nonzero values for an infinite number of charges of the asymptotic $ {\mathcal{W}_\infty }\left[ \lambda \right] $ symmetry. Applying a previously developed set of rules for ensuring smooth solutions, we compute the black hole partition function perturbatively in the chemical potential. At λ = 0, 1 we compare our result against boundary CFT computations involving free bosons and fermions, and find perfect agreement. For generic λ we expect that our gravity result will match the partition function of the coset CFTs conjectured by Gaberdiel and Gopakumar to be dual to these bulk theories.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f25b1047e27d8aa2c92e647f8538d73f13e5e40e

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Citations in the corpus

Thermodynamics of higher spin black holes in 3D (2012, methodology): “Such a computation could be performed along the lines of [40, 49], perhaps first using the free field representation of the W((2)) 3 algebra as a possible starting point [54].”
Minimal model holography (2012, methodology): “The mass, angular momentum and charges of the black hole were computed and used to infer the free energy [92], log ZBH(τ̂ , α) = iπc 12 τ̂ [ 1 − 4 3 α2 τ̂ 4 + 400 27 λ2 − 7 λ2 − 4 α4 τ̂ 8 − 1600 27 5λ4 − 85λ2 + 377 (λ2 − 4)2 α6 τ̂ 12 + · · · ]”
Thermodynamics of higher spin black holes in AdS3 (2013, background): “In the present context, this observation might help us understand why the CFT computations of [18, 43] are in agreement with the entropy as computed in the holomorphic formulation, rather than its canonical version.”
Black holes and singularity resolution in higher spin gravity (2011, background): “All known black hole solutions of the theory, including those described recently by [14, 15, 16, 17], can be constructed in this manner.”
Higher spin gravity in 3D: Black holes, global charges and thermodynamics (2012, background): “28 44 v2 [ he p- th ] 5 S ep 2 01 3 Global charges and thermodynamic properties of three-dimensional higher spin black holes that have been recently found in the literature are revisited.”
Higher spin black holes from CFT (2012, methodology): “) Black hole solutions in this theory were constructed in [26].”
Black holes in three dimensional higher spin gravity: a review (2012, methodology): “Consequently, the holographic calculation of the partition functions produces nontrivial predictions on the CFT side [72,73], which can be checked by direct CFT calculations [74] when a CFT with the right symmetries and large central charge is available.”
Bounding the space of holographic CFTs with chaos (2016, background): “Our results suggest that the higher spin black holes of [101], with an infinite tower of higher spin charges, cannot be formed in Vasiliev theory by throwing higher spin quanta into a BTZ black hole.”
Scalar fields and three-point functions in D = 3 higher spin gravity (2011, methodology): “4) This was originally presented in an early paper on W∞ algebras [26], and used more recently by two of the present authors [23] to compute black hole partition functions in hs[λ] gravity.”
Conical defects in higher spin theories (2011, background): “Further, in [30], the resulting thermodynamic partition function in the bulk (with chemical potential for the spin-3 charge) was successfully compared with the prediction from the large N CFTs (1.”
Generalized black holes in three-dimensional spacetime (2014, background): “However this interpretation leads to conflicting results when its entropy was evaluated [22, 23, 30–42, 68].”