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

Abstract

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