Dimensional reduction of the massless limit of the linearized "New Massive Gravity"

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.

12 pages, one more reference and text slightly modified accordingly

References in corpus (5)

• Massive Gravity in Three Dimensions
• More on Massive 3D Gravity
• Ghost-free, finite, fourth order D=3 (alas) gravity
• Deconstructing Dimensions and Massive Gravity
• Dimensional reduction as a method to obtain dual theories for massive spin two in arbitray dimensions

Cited by in corpus (3)

• The dimensional reduction of linearized spin-2 theories invariant under transverse diffeomorphisms
• On the Perturbative Quantization of Einstein-Hilbert Gravity Embedded in a Higher Derivative Model
• Self-dual models in $D=2+1$ from dimensional reduction