Two-column higher spin massless fields in AdS(d)

TL;DR

This work develops a manifestly covariant framework for free massless mixed-symmetry fields in $AdS_d$ corresponding to arbitrary two-column Young tableaux, using the Ashtekar–Sen–Vasiliev approach of framing these fields as gauge $p$-forms valued in $so(d-1,2)$. By introducing a physical $p$-form $e^{a[s]}_{(p)}$ and an auxiliary $p$-form $\omega^{a[s+1]}_{(p)}$, the authors derive a gauge-invariant action of MacDowell–Mansouri type and perform a Lorentz-covariant decomposition of the resulting curvatures to identify primary and secondary Weyl tensors that encode the dynamical degrees of freedom. The resulting equations of motion eliminate the auxiliary field and reduce to a second-order differential operator acting on the physical field, matching known covariant two-column higher-spin equations in $AdS_d$ (and reproducing Metsaev’s form upon appropriate specialization). In the flat limit, an enhanced gauge symmetry emerges, which can be realized via a Stueckelberg mechanism, leading to a decomposition into independent higher-spin fields; the framework also suggests possible dual Minkowski descriptions of certain AdS fields. Overall, the paper establishes a concrete, covariant, and potentially duality-rich description of two-column higher-spin massless fields in $AdS_d$.

Abstract

Particular class of AdS(d) mixed-symmetry bosonic massless fields corresponding to arbitrary two-column Young tableaux is considered. Unique gauge invariant free actions are found and equations of motion are analyzed.