The dimensional reduction of linearized spin-2 theories invariant under transverse diffeomorphisms

Author(s)

Dalmazi, D. ^[1] ; dos Santos, R. R. Lino ^{[1, 2]}

Affiliation

^[1] UNESP, Dept Fis, Campus Guaratingueta, BR-12516410 Guaratingueta, SP - Brazil

^[2] Univ Southern Denmark, CP3 Origins, Campusvej 55, DK-5230 Campusvej M - Denmark

• Document type: Journal article
• Source: EUROPEAN PHYSICAL JOURNAL C; v. 81, n. 6 JUN 2021.
• Web of Science Citations: 0

Abstract

Here we perform the Kaluza-Klein dimensional reduction from D+1 to D dimensions of massless Lagrangians described by a symmetric rank-2 tensor and invariant under transverse differmorphisms (TDiff). They include the linearized Einstein-Hilbert theory, linearized unimodular gravity and scalar tensor models. We obtain simple expressions in terms of gauge invariant field combinations and show that unitarity is preserved in all cases. After fixing a gauge, the reduced model becomes a massive scalar tensor theory. We show that the diffeomorphism (Diff) symmetry, instead of TDiff, is a general feature of the massless sector of consistent massive scalar tensor models. We discuss some subtleties when eliminating Stuckelberg fields directly at action level as gauge conditions. A non local connection between the massless sector of the scalar tensor theory and the pure tensor TDiff model leads to a parametrization of the non conserved source which naturally separates spin-0 and spin-2 contributions in the pure tensor theory. The case of curved backgrounds is also investigated. If we truncate the non minimal couplings to linear terms in the curvature, vector and scalar constraints require Einstein spaces as in the Diff and WTDiff (Weyl plus Diff) cases. We prove that our linearized massive scalar tensor models admit those curved background extensions. (AU)

• FAPESP's process: 18/24767-2 - Transverse diffeomorphisms and spin-2 particles
• Grantee: Rafael Robson Lino dos Santos
• Support Opportunities: Scholarships in Brazil - Master