Model of Persistent Breaking of Discrete Symmetry

Area of Science:

• Theoretical physics
• High-energy physics
• Condensed matter theory

Background:

• Symmetry breaking is crucial in understanding fundamental forces and condensed matter phases.
• The Coleman-Hohenberg-Mermin-Wagner theorem typically prohibits spontaneous symmetry breaking in 2D systems at finite temperatures.
• Previous work has explored bypassing this theorem in specific models.

Purpose of the Study:

• To construct and analyze UV-complete field-theoretic models exhibiting spontaneous global symmetry breaking at arbitrarily high temperatures.
• To investigate the behavior of a specific conformal vector model with O(N)×Z_{2} symmetry.
• To explore the implications for the Coleman-Hohenberg-Mermin-Wagner theorem in 2+1 dimensions.

Main Methods:

• Utilizing conformal perturbation theory to analyze symmetry breaking at finite temperatures.
• Examining a conformal vector model with O(N)×Z_{2} symmetry.
• Investigating the model in general dimensions, including 2+1 dimensions.

Main Results:

• The Z_{2} symmetry is shown to be broken at finite temperatures for N>17.
• In the infinite N limit, the model possesses a nontrivial conformal manifold that deforms at finite temperature.
• The model exhibits persistent breaking of O(N) symmetry in 2+1 dimensions at finite temperatures.

Conclusions:

• The study provides examples of UV-complete field theories where spontaneous global symmetry breaking persists to arbitrarily high temperatures.
• The findings offer a new scenario bypassing the Coleman-Hohenberg-Mermin-Wagner theorem in 2+1 dimensions.
• The deformation of the conformal manifold at finite temperature is a key feature of the model.