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 are shown to describe localization on ``branes'' of different dimensions embedded into the generalized space-time $\M_M$ with matrix (i.e., ``central charge'') coordinates. The case of bilinear tensor product is considered in detail. The conserved currents built from bilinears of rank 1 fields in $\M_M$ are shown to satisfy the field equations of the rank 2 fields in $\M_M$. Also, the rank 2 fields in $\M_M$ are shown to be equivalent to the rank 1 fields in $\M_{2M}$.

27 pages, latex, no figures. V2: references and one comment added. V3: typos corrected V4: minor correction, one reference and some explanations added, the version to appear in Theor.Math.Phys

References in corpus (1)

• AdS/CFT Dualities and the Unitary Representations of Non-compact Groups and Supergroups: Wigner versus Dirac

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