1108.0225 (Werner Ruehl)

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

Werner Ruehl

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.

View original: http://arxiv.org/abs/1108.0225