p-form symmetry

A continuous one is associated with a conserved $(p+1)$-form current:
$d\star J^{(p+1)}=0$ charge: $Q^{(p)}={\int }_{{\mathrm{\Sigma }}_{d-p-1}}\star J^{(p+1)}$
eg. Maxwell in 4d
$\star J_e^{(2)}=\frac{i}{e^2}\star F^{(2)}=\frac{i}{e^2}D{A}_D,\star J_m^{(2)}=\frac{1}{2\pi }{F}^{(2)}$
$A\to A+\lambda$ with $d\lambda =0$, where $\lambda$ is a globally defined closed 1-form, while gauge transformation is $A\to A+d{\lambda }^{\prime }$ (exact 1-form)