Charges in nonlinear higher-spin theory

• Published in: The journal of high energy physics Vol. 2017; no. 3; pp. 1 - 24
• Main Authors: Didenko, V. E., Misuna, N. G., Vasiliev, M. A.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2017; Springer Nature B.V; SpringerOpen
• Subjects: Black Holes; Chemical potential; Classical and Quantum Gravitation; Elementary Particles; High energy physics; Higher Spin Gravity; Higher Spin Symmetry; Integrals; Mathematical analysis; Nonlinearity; Partitions; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity; Relativity Theory; String Theory; Tensors; Topology; Higher Spin Gravity; Black Holes; Higher Spin Symmetry
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP03(2017)164

A bstract Nonlinear higher-spin equations in four dimensions admit a closed two-form that defines a gauge-invariant global charge as an integral over a two-dimensional cycle. In this paper we argue that this charge gives rise to partitions depending on various lower- and higher-spin chemical potentials identified with modules of topological fields in the theory. The vacuum contribution to the partition is calculated to the first nontrivial order for a solution to higher-spin equations that generalizes AdS 4 Kerr black hole of General Relativity. The resulting partition is non-zero being in parametric agreement with the ADM-like behavior of a rotating source. The linear response of chemical potentials to the partition function is also extracted. The explicit unfolded form of 4 d GR black holes is given. An explicit formula relating asymptotic higher-spin charges expressed in terms of the generalized higher-spin Weyl tensor with those expressed in terms of Fronsdal fields is obtained.