We show there exist UV-complete field-theoretic models in general dimension, including 2+1, with the spontaneous breaking of a global symmetry, which persists to the arbitrarily high temperatures. Our example is a conformal vector model with the O(N)×Z2 symmetry at zero temperature. Using conformal perturbation theory we establish Z2 symmetry is broken at finite temperature for N>17. Similar to recent constructions of [N. Chai , Phys. Rev. D 102, 065014 (2020).PRVDAQ2470-001010.1103/PhysRevD.102.065014, N. Chai , Phys. Rev. Lett. 125, 131603 (2020).PRLTAO0031-900710.1103/PhysRevLett.125.131603], in the infinite N limit our model has a nontrivial conformal manifold, a moduli space of vacua, which gets deformed at finite temperature. Furthermore, in this regime the model admits a persistent breaking of O(N) in 2+1 dimensions, therefore providing another example where the Coleman-Hohenberg-Mermin-Wagner theorem can be bypassed.
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We thank Alex Avdoshkin, Dean Carmi, Soumyadeep Chaudhuri, Changha Choi, Joshua Feinberg, Mikhail Goykhman, Eliezer Rabinovici, Ritam Sinha, and especially Zohar Komargodski for helpful discussions and correspondence. This work is partially supported by the Binational Science Foundation (Grant No. 2016186). A. D. is grateful to Weizmann Institute of Science for hospitality and acknowledges sabbatical support of the Schwartz/Reisman Institute for Theoretical Physics. N. C. and M. S. are grateful to the Israeli Science Foundation Center of Excellence (Grant No. 2289/18) and the Quantum Universe I-CORE program of the Israel Planning and Budgeting Committee (Grant No. 1937/12) for continuous support of our research. N. C. is grateful for the support from the Yuri Milner scholarship.
Published by the American Physical Society