TL;DR
This paper explores how Fronsdal fields in AdS$_3$ can be decomposed into a finite set of modes in AdS$_2$, revealing a spectrum of massive Klein-Gordon and Proca fields through a detailed mode analysis.
Contribution
It introduces a novel dimensional degression approach for Fronsdal fields in AdS$_3$, resulting in a finite Kaluza-Klein spectrum in AdS$_2$.
Findings
Finite Kaluza-Klein spectrum in AdS$_2$
Spectrum includes massive Klein-Gordon and Proca fields
Uses mode expansion, gauge fixing, and Schouten identities
Abstract
We analyze the Kaluza-Klein type procedure in AdS space called the dimensional degression. The topological theory of the Fronsdal field in AdS is reformulated in terms of the fields propagating in AdS. We find that the Fronsdal field in AdS leads to finitely many Kaluza-Klein modes. Namely, the obtained spectrum is the massive Klein-Gordon and Proca fields in AdS. The result is derived by using the specific mode expansion, the gauge fixing, and 2-dimensional Schouten identities.
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