Conformal Higher-Spin Gravity: Linearized Spectrum = Symmetry Algebra

Abstract

The linearized spectrum and the algebra of global symmetries of conformal higher-spin gravity decompose into infinitely many representations of the conformal algebra. Their characters involve divergent sums over spins. We propose a suitable regularization adapted to their evaluation and observe that their characters are actually equal. This result holds in the case of type-A and type-B (and their higher-depth generalizations) theories and confirms previous observations on a remarkable rearrangement of dynamical degrees of freedom in conformal higher-spin gravity after regularization.

47 pages, 1 figures; v2: references and appendix D on formal CHS theory (Segal's formulation) added