Generalized soldering of $\pm 2$ helicity states in $D=2+1$

Abstract

The direct sum of a couple of Maxwell-Chern-Simons (MCS) gauge theories of opposite helicities $\pm 1$ does not lead to a Proca theory in $D=2+1$, although both theories share the same spectrum. However, it is known that by adding an interference term between both helicities we can join the complementary pieces together and obtain the physically expected result. A generalized soldering procedure can be defined to generate the missing interference term. Here we show that the same procedure can be applied to join together $\pm 2$ helicity states in a full off-shell manner. In particular, by using second-order (in derivatives) self-dual models of helicities $\pm 2$ (spin two analogues of MCS models) the Fierz-Pauli theory is obtained after soldering. Remarkably, if we replace the second-order models by third-order self-dual models (linearized topologically massive gravity) of opposite helicities we end up after soldering exactly with the new massive gravity theory of Bergshoeff, Hohm and Townsend in its linearized approximation.

arXiv comment12 pages, to appear in Phys. Rev. D

References in corpus (12)

• Massive Gravity in Three Dimensions
• More on Massive 3D Gravity
• On Unitarity of Massive Gravity in Three Dimensions
• Bose Symmetry and Chiral Decomposition of 2D Fermionic Determinants
• Self-duality and soldering in odd dimensions
• Dual descriptions of spin two massive particles in $D=2+1$ via master actions
• On Soldering Chiralities
• Generalizing the Soldering procedure
• Interference of Spin-2 Self-Dual Modes
• Massive Vector Chern-Simons Gravity
• On the Coupling Problem of Higher Spin Fields in 2+1 Dimension
• Studies in certain planar field theories

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• New Massive Supergravity and Auxiliary Fields
• On higher spin analogues of linearized Topologically Massive Gravity and linearized "New Massive Gravity"
• Higher order self-dual models for spin-3 particles in $D=2+1$
• Soldering spin-3/2 fermions in $D=2+1$
• Soldering spin-3 opposite helicities in $D=2+1$
• Master actions for linearized massive gravity models in 3-D
• Classical electrodynamics and gauge symmetry of the X-boson
• Some considerations on duality concerning kappa-Minkowski spacetime theories
• Dual composition of odd-dimensional models
• Self-dual models in $D=2+1$ from dimensional reduction
• Effects of curvature and gravity from flat spacetime