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

M. A. Vasiliev^a, O. A. Gelfond<sup>b

a</sup> P. N. Lebedev Physical Institute, Russian Academy of Sciences
^b Scientific Research Institute for System Studies of RAS

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 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 $\mathcal M_{2M}$.

Keywords: higher-spin fields, higher symmetries.

Received: 31.01.2005

DOI: 10.4213/tmf1880

 English version: Theoretical and Mathematical Physics, 2005, 145:1, 1400–1424

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