Dimensional reduction of the massless limit of the linearized ‘New Massive Gravity’

H A Biazotti,D Dalmazi,G B De Gracia

doi:10.1140/epjc/s10052-014-2747-0

H A Biazotti, D Dalmazi + Show 1 more

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https://doi.org/10.1140/epjc/s10052-014-2747-0

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Abstract

The so called "New Massive Gravity" in $D=2+1$ consists of the Einstein-Hilbert action (with minus sign) plus a quadratic term in curvatures ($K$-term). Here we perform the Kaluza-Klein dimensional reduction of the linearized $K$-term to $D=1+1$. We end up with a fourth-order massive electrodynamics in $D=1+1$ described by a rank-2 tensor. Remarkably, there appears a local symmetry in $D=1+1$ which persists even after gauging away the Stueckelberg fields of the dimensional reduction. It plays the role of a $U(1)$ gauge symmetry. Although of higher-order in derivatives, the new $2D$ massive electrodynamics is ghost free, as we show here. It is shown, via master action, to be dual to the Maxwell-Proca theory with a scalar Stueckelberg field.

Highlights

The authors of [1] have suggested an invariant theory under general coordinate transformations which describes a massive spin-2 particle in D = 2 + 1
We show here that the linearized K -term is reduced to a kind of higher-derivative massive 2D electrodynamics, which is in agreement with the fact that the linearized K -term is dual to the Maxwell theory in 3D as shown in [5]; see [2] and [6]
Since massless particles in D dimensions have the same number of degrees of freedom as massive particles in D − 1 dimensions, one might wonder whether the ‘New Massive Gravity’ (NMG) theory might be regarded as a dimensional reduction of some fourth-order massless spin-2 model in D = 3+1, which would be certainly interesting from the point of view of renormalizable quantum gravity in D = 3 + 1

Summary

Introduction

Page 3 of 7 2747 where hμν = hμν + (∂μφν + ∂ν φμ)/m − ∂μ∂ν H/m2 is the only local combination of those fields invariant under the reduced reparametrization symmetry given in (12)–(14) with. Note that the 2D symmetries (12)–(14) allow us to gauge away the Stueckelberg fields: φμ = 0 = H such that S2D[hμν ] → S2D[hμν ] which is still invariant under δhμν = (ημν − ∂μ∂ν/m2). This is rather surprising since local symmetries in dimensionally reduced massive theories usually disappear altogether with the Stueckelberg fields.

Equations of motion

Propagator and absence of ghosts

Master action and duality

Conclusion