  Recently the ETH group has reported an experiment on superradiant transition
of a Bose condensate in two crossed beam cavities. The surprise is that they
find that across the superradiant transition, the cavity light can be emitted
in any superposition of these two cavity modes. This indicates an additional
$U(1)$ symmetry that does not exist in the full Hamiltonian. In this letter we
show that this symmetry is an emergent symmetry in the vicinity of the phase
transition. We identify all the necessary conditions that are required for this
emergent $U(1)$ symmetry and show that the ETH experiment is a special case
that satisfies these conditions. We further show that the superradiant
transition in this system can also be driven to a first order one when the
system is tuned away from the point having the emergent symmetry.
