Gauge Non-Invariant Higher-Spin Currents in $4d$ Minkowski Space

Abstract

Conserved currents of any spin $t>0$ built from symmetric massless gauge fields of any integer spin $s\ge t$ in {4d} Minkowski space are found. In particular, stress-energy tensor for a higher-spin field of any spin is constructed. Analogously to spin-two stress (pseudo)tensor, currents considered in this paper are not gauge invariant. However, they are shown to generate gauge invariant conserved charges. Besides expected parity even HS currents, we found unexpected parity odd currents that generate less symmetries than the even ones. It is argued that these odd currents unlikely admit a consistent $AdS$ deformation.

17 pages; V2: Minor corrections, the version published in the volume in honor of Andrei Alekseevich Slavnov

References in corpus (2)

• Cubic Vertices for Symmetric Higher-Spin Gauge Fields in $(A)d{S}_d$
• Higher spin interactions with scalar matter on constant curvature spacetimes: conserved current and cubic coupling generating functions

Cited by in corpus (2)

• Current Interactions from the One-Form Sector of Nonlinear Higher-Spin Equations
• Higher Spin Gravities and Presymplectic AKSZ Models