Frame-like off-shell dualisation for mixed-symmetry gauge fields

Abstract

We construct a purely frame-like parent action that allows to dualise, at the off-shell level, an arbitrary mixed-symmetry bosonic massless fields in Minkowski background of dimensions d. Starting from any massless mixed-symmetry gauge field in the standard Skvortsov frame-like formulation and following an off-shell dualisation procedure, we obtain dual theories which are on-shell related by so(d-2) Hodge duality. The Hodge dualisation can be done on any column of the Young diagram characterizing the generalised spin of the original frame-like field. Dualisation with respect to the first column of the Young diagram leads to a standard frame-like action for the dual field. Any other dualisation results in an action which cannot be described by the standard frame-like formalism, as the on-shell field is not so(d-2) traceless. Instead, the latter field is given by the product of an irreducible traceless tensor and a certain number of so(d-2)-invariant metrics, and the corresponding dual frame-like action is new. Such actions require supplementary fields, which naturally arise along the lines of the approach that we propose.

28 pages, no figure, references added. Expanded version of the invited contribution to the J.Phys.A special volume on "Higher Spin Theories and AdS/CFT" edited by Matthias Gaberdiel and Mikhail Vasiliev

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Cited by in corpus (5)

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• Mixed-symmetry multiplets and higher-spin curvatures
• Prepotentials for linearized supergravity
• Massive two-column bosonic fields in the frame-like formalism
• Gauge fields and infinite chains of dualities