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

TL;DR

This paper discovers an infinite set of higher spin conserved charges in $sp(2M)$ symmetric spacetime, which generate new higher spin conformal currents in Minkowski spacetime, revealing deep symmetries and invariants in higher-dimensional field theories.

Contribution

The work constructs an infinite set of conserved higher spin charges in $sp(2M)$ symmetric spacetime, linking them to conformal currents in Minkowski space and providing a new invariant bilinear form for solutions.

Findings

Found infinite higher spin conserved charges in $sp(2M)$ symmetric systems.

Generated infinite towers of higher spin conformal currents in Minkowski spacetime.

Established a positive definite norm on the space of quantum states.

Abstract

Infinite 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.