A 2+1 dimensional QFT is constructed whose parity symmetry is unbroken at zero temperature but spontaneously breaks at all sufficiently high temperatures.
Thermal order in holographic CFTs and no-hair theorem violation in black branes
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We present a large class of holographic models where the boundary ${\mathbb R}^{2,1}$ dimensional conformal field theory has a thermal phase with a spontaneously broken global symmetry. The dual black branes in a Poincare patch of asymptotically $AdS_4$ violate the no-hair theorem.
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Spontaneous Space-Time Parity Breaking Without Thermal Restoration
A 2+1 dimensional QFT is constructed whose parity symmetry is unbroken at zero temperature but spontaneously breaks at all sufficiently high temperatures.