On Dimensional Degression in AdS(d)

TL;DR

This paper introduces and analyzes dimensional degression, a novel method relating fields in higher and lower dimensional anti-de Sitter spaces, with group-theoretic and field-theoretic approaches for various fields.

Contribution

It develops a group-theoretic and field-theoretic framework for dimensional degression in AdS spaces, extending previous results and analyzing mass spectra for multiple field types.

Findings

Mass spectra of fields in AdS(d) derived from higher-dimensional fields.

Extension of Metsaev's results to the shadow sector for scalar fields.

Group-theoretic classification of symmetric bosonic and fermionic representations.

Abstract

We analyze the pattern of fields in d+1 dimensional anti-de Sitter space in terms of those in d dimensional anti-de Sitter space. The procedure, which is neither dimensional reduction nor dimensional compactification, is called dimensional degression. The analysis is performed group-theoretically for all totally symmetric bosonic and fermionic representations of the anti-de Sitter algebra. The field-theoretical analysis is done for a massive scalar field in AdS(d+d$^\prime$) and massless spin one-half, spin one, and spin two fields in AdS(d+1). The mass spectra of the resulting towers of fields in AdS(d) are found. For the scalar field case, the obtained results extend to the shadow sector those obtained by Metsaev in [1] by a different method.