On the relation between local and geometric Lagrangians for higher spins

Abstract

Equations of motion for free higher-spin gauge fields of any symmetry can be formulated in terms of linearised curvatures. On the other hand, gauge invariance alone does not fix the form of the corresponding actions which, in addition, either contain higher derivatives or involve inverse powers of the d'Alembertian operator, thus introducing possible subtleties in degrees of freedom count. We suggest a path to avoid ambiguities, starting from local, unconstrained Lagrangians previously proposed, and integrating out the auxiliary fields from the functional integral, thus generating a unique non-local theory expressed in terms of curvatures.

14 pages. Contribution to the proceedings of the 1st Mediterranean Conference on Classical and Quantum Gravity, Kolymbary (Crete, Greece) September 14-18 2009

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• On the Structure of Quartic Vertices for Massless Higher Spin Fields on Minkowski Background
• Spinning Witten Diagrams
• Maxwell-like Lagrangians for higher spins
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• Arbitrary spin conformal fields in (A)dS
• Interactions in Higher-Spin Gravity: a Holographic Perspective
• Generalised connections and higher-spin equations
• Half-integer Higher Spin Fields in (A)dS from Spinning Particle Models
• Low-spin models for higher-spin Lagrangians
• Supersymmetric Reducible Higher-Spin Multiplets in Various Dimensions
• One-loop effective actions and higher spins
• Mixed-symmetry multiplets and higher-spin curvatures
• One-loop effective actions and higher spins. II
• CFT adapted approach to massless fermionic fields, AdS/CFT, and fermionic conformal fields
• Lectures on Higher Spin Holography
• Lagrangian formulation of massive fermionic higher spin fields on a constant electromagnetic background
• On Tensorial Spaces and BCFW Recursion Relations for Higher Spin Fields
• Light-cone gauge approach to arbitrary spin fields, currents, and shadows
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• Massive higher spin fields in curved spacetime and necessity of non-minimal couplings