Conformal current ($j^{\mu }={\Theta }^{\mu \nu }{\omega }_{\nu }$)

For a symmetric conserved stress-energy tensor $\Theta$ and a Conformal Killing vector field $\omega$ in dimension $d$, the displayed conformal current has divergence $(\partial \cdot \omega ){\Theta }^{\mu }{}_{\mu }/d$. This follows by contracting the Conformal Killing equation with $\Theta$. A traceless tensor therefore gives a conserved current for every conformal generator.