Charges in nonlinear higher-spin theory

TL;DR

This paper explores gauge-invariant charges in nonlinear higher-spin theory, linking them to partition functions and analyzing their behavior in solutions generalizing AdS4 Kerr black holes, with implications for understanding higher-spin black hole properties.

Contribution

It introduces a gauge-invariant charge framework in higher-spin theory, calculates the first-order vacuum contribution for generalized black hole solutions, and relates higher-spin charges to Fronsdal fields.

Findings

Partition function depends on higher- and lower-spin chemical potentials.

Vacuum contribution to the partition is non-zero and matches ADM-like behavior.

Explicit formulas relate higher-spin charges to Weyl and Fronsdal fields.

Abstract

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 AdS4 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 4d 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.