On Higher Derivatives in 3D Gravity and Higher Spin Gauge Theories

Abstract

The general second-order massive field equations for arbitrary positive integer spin in three spacetime dimensions, and their "self-dual" limit to first-order equations, are shown to be equivalent to gauge-invariant higher-derivative field equations. We recover most known equivalences for spins 1 and 2, and find some new ones. In particular, we find a non-unitary massive 3D gravity theory with a 5th order term obtained by contraction of the Ricci and Cotton tensors; this term is part of an N=2 super-invariant that includes the "extended Chern-Simons" term of 3D electrodynamics. We also find a new unitary 6th order gauge theory for "self-dual" spin 3.

23 pp. New references, improved spin-3 discussion. Minor additional corrections in v3

References in corpus (6)

• Massive Gravity in Three Dimensions
• More on Massive 3D Gravity
• Ghost-free, finite, fourth order D=3 (alas) gravity
• Massive 3D Supergravity
• A new spin-2 self-dual model in $D=2+1$
• Dual descriptions of spin two massive particles in $D=2+1$ via master actions

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