AdS${}_3$/AdS${}_2$ degression of Fronsdal fields

Abstract

We analyze the Kaluza-Klein type procedure in AdS${}_3$ space called the dimensional degression. The topological theory of the Fronsdal field in AdS${}_3$ is reformulated in terms of the fields propagating in AdS${}_2$. We find that the Fronsdal field in AdS${}_3$ leads to finitely many Kaluza-Klein modes. Namely, the obtained spectrum is the massive Klein-Gordon and Proca fields in AdS${}_2$. The result is derived by using the specific mode expansion, the gauge fixing, and 2-dimensional Schouten identities.

v2: 24 pages, Appendix E added, typos fixed

References in corpus (2)

• Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields
• On Dimensional Degression in AdS(d)