  The possibility of a superradiant phase transition in light-matter systems is
the subject of much debate, due to numerous apparently conflicting no-go and
counter no-go theorems. Using an arbitrary gauge approach we show that a unique
phase transition does occur in archetypal many-dipole cavity QED systems, and
that it manifests unambiguously via a macroscopic gauge-invariant polarisation.
We find that the gauge choice controls the extent to which this polarisation is
included as part of the radiative quantum subsystem and thereby determines the
degree to which the abnormal phase is classed as superradiant. This resolves
the long-standing paradox of no-go and counter no-go theorems for
superradiance, which are shown to refer to different definitions of radiation.
