  Phase transitions associated with nearly conformal dynamics are known to lead
to significant supercooling. A notorious example is the phase transition in
Randall-Sundrum models or their CFT duals. In fact, it was found that the phase
transition in this case is first-order and the tunneling probability for the
radion/dilaton is so small that the system typically remains trapped in the
false vacuum and the phase transition never completes. The universe then keeps
expanding and cooling. Eventually the temperature drops below the QCD scale. We
show that the QCD condensates which subsequently form give an additional
contribution to the radion/dilaton potential, an effect which had been ignored
so far. This significantly reduces the barrier in the potential and allows the
phase transition to complete in a substantially larger region of parameter
space. Due to the supercooling, electroweak symmetry is then broken
simultaneously. This class of models therefore naturally leads to an
electroweak phase transition taking place at or below QCD temperatures, with
interesting cosmological implications and signatures.
