Aspects of Emergent Symmetries

TL;DR

This review explores how emergent symmetries like Lorentz invariance and supersymmetry appear in low-energy sectors of complex systems across various fields, highlighting their physical significance and potential to address fundamental problems.

Contribution

It provides a comprehensive overview of emergent symmetries in physical systems, emphasizing their natural occurrence and relevance in understanding complex phenomena.

Findings

Emergent symmetries can arise in low-energy regimes of many-body systems.

Examples include Lorentz invariance and supersymmetry appearing naturally.

These symmetries offer insights into fundamental physics and complex systems.

Abstract

These are intended to be review notes on emergent symmetries, i.e., symmetries which manifest themselves in specific sectors of energy in many systems. The emphasis is on the physical aspects rather than computation methods. We include some background material and go through more recent problems in field theory, statistical mechanics and condensed matter. These problems illustrate how some important symmetries, such as Lorentz invariance and supersymmetry, usually believed to be fundamental, can arise naturally in low-energy regimes of systems involving a large number of degrees of freedom. The aim is to discuss how these examples could help us to face other complex and fundamental problems.