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

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 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 $\mathcal M_{2M}$.