Self-duality in odd dimensions

Abstract

For spacetime dimension d = 4 k − 1 one may take the “square root” of the Proca equation for a massive antisymmetric tensor field. The result is a “self-dual” field which propagates half as many massive modes. We present a simple supersymmetric model for d = 3. We also discuss other types of odd-dimensional self-duality, in d = 4 k + 1 and in euclidean spaces.