Emergent symmetry and free energy
arXiv:2207.10095
Abstract
Just as spontaneous symmetry breaking can be understood in terms of energy, emergent symmetry (more precisely, its `size' and structure) can also be explained by free energy. In particular, in renormalization group flow to rational conformal field theory, we find infrared symmetry category is realized by consistent modular tensor category with minimal free energy. For demonstration, we study non-unitary theories.
19 pages + 3 Appendices, 5 tables; v2: added proof on "monotonic" decrease of global dimensions under RG flows and comment on the second law of thermodynamics, and fixed typos