  We discuss generalized global symmetries and their breaking. We extend
Goldstone's theorem to higher form symmetries by showing that a perimeter law
for an extended $p$-dimensional defect operator charged under a continuous
$p$-form generalized global symmetry necessarily results in a gapless mode in
the spectrum. We also show that a $p$-form symmetry in a conformal theory in
$2(p+1)$ dimensions has a free realization. In four dimensions this means any
1-form symmetry in a $CFT_4$ can be realized by free Maxwell electrodynamics,
i.e. the current can be photonized. The photonized theory has infinitely many
conserved 0-form charges that are constructed by integrating the symmetry
currents against suitable 1-forms. We study these charges by developing a
twistor-based formalism that is a 4d analogue of the usual holomorphic complex
analysis familiar in $CFT_2$. The charges are shown to obey an algebra with
central extension, which is an analogue of the 2d Abelian Kac-Moody algebra for
higher form symmetries.
