Higher-Rank Conformal Fields in the Sp(2M)-Symmetric Generalized Space-Time

Abstract

We study various Sp(2M)-invariant field equations corresponding to rank-r tensor products of the Fock (singleton) representation of Sp(2M). These equations describe localization on “branes” of different dimensions embedded in the generalized space-time \(\mathcal{M}_M\) with matrix (i.e., “central charge”) coordinates. We consider the case of a bilinear tensor product in detail and show that the conserved currents built from bilinears of rank-1 fields in \(\mathcal{M}_M\) satisfy the field equations for rank-2 fields in \(\mathcal{M}_M\). We also show that rank-2 fields in \(\mathcal{M}_M\) are equivalent to rank-1 fields in \(\mathcal{M}_{2M}\).