Higher Spin Conserved Currents in Sp(2M) Symmetric Spacetime

Abstract

An infinite set of higher spin conserved charges is found for the sp(2M) symmetric dynamical systems in M(M+ 1)/2-dimensional generalized spacetime ℳM. Since the dynamics in ℳM 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 ℳM 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 Σ ⊂ ℳM 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.