Extremal higher spin black holes
Abstract
The gauge sector of three-dimensional higher spin gravities can be formulated as a Chern-Simons theory. In this context, a higher spin black hole corresponds to a flat connection with suitable holonomy (smoothness) conditions which are consistent with the properties of a generalized thermal ensemble. Building on these ideas, we discuss a definition of black hole extremality which is appropriate to the topological character of 3 d higher spin theories. Our definition can be phrased in terms of the Jordan class of the holonomy around a non-contractible (angular) cycle, and we show that it is compatible with the zero-temperature limit of smooth black hole solutions. While this notion of extremality does not require supersymmetry, we exemplify its consequences in the context of sl(3|2) ⊕ sl(3|2) Chern-Simons theory and show that, as usual, not all extremal solutions preserve supersymmetries. Remarkably, we find in addition that the higher spin setup allows for non-extremal supersymmetric black hole solutions. Furthermore, we discuss our results from the perspective of the holographic duality between sl(3|2) ⊕ sl(3|2) Chern-Simons theory and two-dimensional CFTs with W (3|2) symmetry, the simplest higher spin extension of the N = 2 super-Virasoro algebra. In particular, we compute W (3|2) BPS bounds at the full quantum level, and relate their semiclassical limit to extremal black hole or conical defect solutions in the 3 d bulk. Along the way, we discuss the role of the spectral flow automorphism and provide a conjecture for the form of the semiclassical BPS bounds in general N = 2 two-dimensional CFTs with extended symmetry algebras.
- Publication:
-
Journal of High Energy Physics
- Pub Date:
- April 2016
- DOI:
- 10.1007/JHEP04(2016)077
- arXiv:
- arXiv:1512.00073
- Bibcode:
- 2016JHEP...04..077B
- Keywords:
-
- AdS-CFT Correspondence;
- Black Holes;
- Conformal and W Symmetry;
- Higher Spin Gravity;
- High Energy Physics - Theory;
- General Relativity and Quantum Cosmology
- E-Print:
- 63 + 18 pages, 2 figures. v2: typos corrected, minor rewording in the abstract for improved clarity, version published in JHEP