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22 October 2021
  » arxiv » hep-th/0204167

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Higher Spin Conserved Currents in $Sp(2M)$ Symmetric Spacetime
M.A. Vasiliev ;
Date 19 Apr 2002
Journal Russ.Phys.J. 45 (2002) 670-681; Izv.Vuz.Fiz. 2002N7 (2002) 23-34
Subject hep-th
AbstractInfinite set of higher spin conserved charges is found for the $sp(2M)$ symmetric dynamical systems in $f{1}{2} M (M+1)$-dimensional generalized spacetime $M_M$. Since the dynamics in $M_M$ is equivalent to the conformal dynamics of infinite towers of fields in $d$-dimensional Minkowski spacetime with $d=3,4,6,10,...$ for $M=2,4,8,16, ...$, respectively, the constructed currents in $M_M$ generate infinite towers of (mostly new) higher spin conformal currents in Minkowski spacetime. The charges have a form of integrals of $M$-forms which are bilinear in the field variables and are closed as a consequence of the field equations. Conservation implies independence of a value of charge of a local variation of a $M$-dimensional integration surface $Sigma subset M_M$ analogous to Cauchy surface in the usual spacetime. The scalar conserved charge provides an invariant bilinear form on the space of solutions of the field equations that gives rise to a positive definite norm on the space of quantum states.
Source arXiv, hep-th/0204167
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