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The so called "New Massive Gravity" in $D=2+1$ consists of theEinstein-Hilbert action (with minus sign) plus a quadratic term in curvatures($K$-term). Here we perform the Kaluza-Klein dimensional reduction of thelinearized $K$-term to $D=1+1$. We end up with a fourth-order massiveelectrodynamics in $D=1+1$ described by a rank-2 tensor. Remarkably, thereappears a local symmetry in $D=1+1$ which persists even after gauging away theStueckelberg fields of the dimensional reduction. It plays the role of a $U(1)$gauge symmetry. Although of higher-order in derivatives, the new $2D$ massiveelectrodynamics 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.

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