Massive "spin-2" theories in arbitrary $D \ge 3$ dimensions

TL;DR

This paper introduces two new families of second order Lagrangians for massive spin-2 particles in arbitrary dimensions, highlighting their properties, dualities, and challenges related to renormalizability.

Contribution

It presents novel nonsymmetric tensor-based Lagrangians for massive spin-2 particles, extending the understanding of their dual descriptions and invariance properties.

Findings

One family is Weyl invariant at zero mass.

In D=3, the massless theory has no particle content.

Antisymmetric part propagates as 1/p^2 at high momentum.

Abstract

Here we show that in arbitrary dimensions $D\ge 3$ there are two families of second order Lagrangians describing massive "spin-2" particles via a nonsymmetric rank-2 tensor. They differ from the usual Fierz-Pauli theory in general. At zero mass one of the families is Weyl invariant. Such massless theory has no particle content in $D=3$ and gives rise, via master action, to a dual higher order (in derivatives) description of massive spin-2 particles in $D=3$ where both the second and the fourth order terms are Weyl invariant, contrary to the linearized New Massive Gravity. However, only the fourth order term is invariant under arbitrary antisymmetric shifts. Consequently, the antisymmetric part of the tensor $e_{[\mu\nu]}$ propagates at large momentum as $1/p^2$ instead of $1/p^4$. So, the same kind of obstacle for the renormalizability of the New Massive Gravity reappears in this nonsymmetric higher order description of massive spin-2 particles.