Emergent symmetry and free energy

TL;DR

This paper explores how emergent symmetry in physical systems can be understood through free energy, especially in the context of renormalization group flow to rational conformal field theories, including non-unitary cases.

Contribution

It introduces a framework linking emergent symmetry structure to minimal free energy in renormalization group flows, extending understanding to non-unitary theories.

Findings

Infrared symmetry category is realized by a modular tensor category with minimal free energy.

Demonstrates the approach in non-unitary theories.

Connects symmetry emergence with free energy minimization.

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.