Boundary values of mixed-symmetry massless fields in AdS space

TL;DR

This paper develops a conformal and gauge covariant boundary value formulation for massless mixed-symmetry fields in AdS space, providing a systematic auxiliary field elimination process and detailed analysis of a rank-3 tensor case.

Contribution

It introduces a manifestly conformal and gauge covariant approach for mixed-symmetry massless fields in AdS, with a systematic auxiliary field elimination method.

Findings

Formulation employs auxiliary fields with a systematic elimination procedure.

Application to the rank-3 tensor field demonstrates the approach.

Results in a concise, potentially minimal, irreducible tensor formulation.

Abstract

We elaborate on the ambient space approach to boundary values of $AdS_{d+1}$ gauge fields and apply it to massless fields of mixed-symmetry type. In the most interesting case of odd-dimensional bulk the respective leading boundary values are conformal gauge fields subject to the invariant equations. Our approach gives a manifestly conformal and gauge covariant formulation for these fields. Although such formulation employs numerous auxiliary fields, it comes with a systematic procedure for their elimination that results in a more concise formulation involving only a reasonable set of auxiliaries, which eventually (at least in principle) can be reduced to the minimal formulation in terms of the irreducible Lorentz tensors. The simplest mixed-symmetry field, namely, the rank-3 tensor associated to the two-row Young diagram, is considered in some details.