A first order nonabelian antisymmetric tensor model with hidden higher symmetry

Abstract

We present a nonabelian complex self-dual antisymmetric tensor model, with gauged internal symmetry, comprising a complex multiplet of massless self-dual antisymmetric tensor fields and its conjugate (interacting with massless Yang-Mills gauge fields). We build the model at the classical level, via a first order formulation, assigning local fields to a component expansion over the Dirac algebra and a basis of internal matrices, with Lorentz and gauge invariance ensured by tracing, and applying an appropriate bilinear form. The full expansion requires auxiliary place-holder fields, which are not potentials, but become curvatures (field strengths) after elimination via their algebraic equations of motion. The component expansion over the Dirac algebra is closed under multiplication by additional internal matrices, which are not gauge group generators, but mix internal components, and link auxiliary curvatures with potentials. The model is shown to be invariant under such transformations, and thus possesses a type of hidden internal symmetry. We analyze the specific case of gauge group $SU(2)\! \times \! U(1)$, and as higher symmetry candidates, we consider both the Lie group $SU(3)$ and the Lie superalgebra $SU(2/1)$ (with the additional matrices acting via Lie brackets, or graded Lie brackets, respectively).