Solving Noether's equations for gauge invariant local Lagrangians of N arbitrary higher even spin fields

Abstract

We consider systems of higher spin gauge fields that are described by a free field Lagrangian and one interaction of arbitrary order $N$ that is local and satisfies abelian gauge invariance. Such "solitary" interactions are derived from Noether potentials solving the Noether equations. They are constructed using a free conformal field theory carried by the same flat space as the higher spin fields. In this field theory we consider $N$-loop functions of conserved, conformally covariant currents, they are UV divergent. The residue of the first order pole in the dimensional regularisation approach to the $N$-loop function is a local differential operator and is free of anomalies, so that current conservation and conformal covariance is maintained. Applying this operator to the higher spin fields, the Noether potential results. We study the cases $N=2,N=3$ and N=4. We argue that our N=3 vertex for any number of derivatives $\Delta$ is identical with the known cubic interaction.

Latex, 36 pages, v.2, references added; v.3 the discussion of conformal invariance added

References in corpus (2)

• Cubic Vertices for Symmetric Higher-Spin Gauge Fields in $(A)d{S}_d$
• Effective action in a higher-spin background

Cited by in corpus (7)

• Cubic Vertices for Symmetric Higher-Spin Gauge Fields in $(A)d{S}_d$
• Superconformal symmetry and maximal supergravity in various dimensions
• Radial Reduction and Cubic Interaction for Higher Spins in (A)dS space
• On special quartic interaction of higher spin gauge fields with scalars and gauge symmetry commutator in the linear approximation
• Extended hamiltonian action for arbitrary spin fields in flat and AdS spaces
• Obstruction to E_{7(7)} Deformation in N=8 Supergravity
• Local cubic vertex functions for three massless higher even spin fields on spaces AdS_D: An analytic approach