Conformal invariance of antisymmetric tensor field theories in any even dimension

TL;DR

This paper classifies all flat-space massless conformally invariant tensor field theories in even dimensions, extending known models and introducing new classes of self-dual tensor theories that couple to chiral fermions.

Contribution

It systematically classifies conformally invariant massless tensor theories in any even dimension and constructs new classes of self-dual tensor models that are conformally invariant.

Findings

Scalar and spinor invariance in all dimensions

Gauge p-tensor invariance only in 2p+2 dimensions

New conformally invariant self-dual tensor classes in even dimensions

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(D,2). We recover in a uniform way the facts that scalars and spinors are invariant in any dimension, and that gauge p-tensors are invariant only in 2 p + 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.