Conformal invariance of antisymmetric tensor field theories in any even dimension

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Abstract Using a theorem of Jackiw and Pi expressing the delicate balance of the spin and the orbital momentum,
 we systematically classify the flat-space massless Lagrangian quantum field
 theories that are invariant under the global conformal group $SO(\DD,2)$.
 We recover in a uniform way the facts that scalars and spinors are invariant in any dimension, and that gauge $\pp$-tensors
 are invariant only in $2\pp+2$ dimensions. This case includes the Maxwell theory in 4 dimensions and the Kalb-Ramond 2-forms
 theory in 6 dimensions.
 We then construct two new classes of Lagrangians extending the Avdeev-Chizhov self-dual tensor model to higher dimensions,
 one class using a symmetric metric and the other a skew metric in internal space. Finally,
 we prove in the same uniform way that both classes are
 conformal invariant in any even dimension. In 4 dimensions, these self-dual tensors naturally couple to the
 chiral Fermions of the standard model.