Spontaneous Space-Time Parity Breaking Without Thermal Restoration

Abstract: We construct an ultraviolet-complete, local, and unitary quantum field theory in 2+1 dimensions that exhibits spontaneous breaking of space-time parity, persisting to arbitrarily high temperatures. The theory is defined by a renormalization group trajectory, triggered by a relevant deformation of a conformal field theory, consisting of a critical biconical vector model and a free massless Dirac fermion. This deformation couples the fermion to the scalar sector, generating a renormalization group flow that terminates at a nontrivial infrared fixed point described by a conformal Gross-Neveu-Yukawa model and a decoupled critical vector model. By construction, the quantum field theory is parity invariant at zero temperature. However, we show that at sufficiently high temperatures, parity symmetry is spontaneously broken and remains so even in the infinite-temperature limit. Our analysis relies on both, perturbative renormalization group techniques in $4!-!\epsilon$ dimensions and functional renormalization group techniques directly in 2+1 dimensions.