Higher-Rank Fields and Currents

Abstract

$Sp(2M)$ invariant field equations in the space ${\mathcal{M}}_M$ with symmetric matrix coordinates are classified. Analogous results are obtained for Minkowski-like subspaces of ${\mathcal{M}}_M$ which include usual $4d$ Minkowski space as a particular case. The constructed equations are associated with the tensor products of the Fock (singleton) representation of $Sp(2M)$ of any rank $\mathbf{r}$. The infinite set of higher-spin conserved currents multilinear in rank-one fields in ${\mathcal{M}}_M$ is found. The associated conserved charges are supported by $(\mathbf{r}M-\frac{\mathbf{r}(\mathbf{r}-1)}{2})-$dimensional differential forms in ${\mathcal{M}}_M$, that are closed by virtue of the rank-$2\mathbf{r}$ field equations. The cohomology groups $H^p({\sigma }_{-}^{\mathbf{r}})$ with all $p$ and $\mathbf{r}$, which determine the form of appropriate gauge fields and their field equations, are found both for ${\mathcal{M}}_M$ and for its Minkowski-like subspace.

27 pages; V2: Significant extension of the results to computation of all ${\sigma }_{-}$ cohomologies, 43 pages; V3: Discussion of equations in generalized Minkowski space from the perspective of usual Minkowski space and reference added, typos corrected, the journal version, 44 pages

References in corpus (3)

• Higher Spin Fields in Siegel Space, Currents and Theta Functions
• CFT adapted approach to massless fermionic fields, AdS/CFT, and fermionic conformal fields
• On-Shell Structures of MHV Amplitudes Beyond the Planar Limit