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Abstract

At the free level, a given massless field can be described by an infinite
number of different potentials related to each other by dualities. In terms of
Young tableaux, dualities replace any number of columns of height $h_i$ by
columns of height $D-2-h_i$, where $D$ is the spacetime dimension: in
particular, applying this operation to empty columns gives rise to potentials
containing an arbitrary number of groups of $D-2$ extra antisymmetric indices.
Using the method of parent actions, action principles including these
potentials, but also extra fields, can be derived from the usual ones. In this
paper, we revisit this off-shell duality and clarify the counting of degrees of
freedom and the role of the extra fields. Among others, we consider the
examples of the double dual graviton in $D=5$ and two cases, one topological
and one dynamical, of exotic dualities leading to spin three fields in $D=3$.