Chiral Random Matrix Theory and Chiral Perturbation Theory

TL;DR

This paper discusses how the connection between chiral Random Matrix Theory and chiral Perturbation Theory enables a first-principles demonstration of spontaneous chiral symmetry breaking in QCD through lattice simulations.

Contribution

It introduces the link between chiral Random Matrix Theory and chiral Perturbation Theory, providing a new way to confirm chiral symmetry breaking from fundamental principles.

Findings

Chiral Random Matrix Theory matches low-energy QCD predictions.

Lattice simulations confirm the theoretical connection.

Spontaneous chiral symmetry breaking can be demonstrated from first principles.

Abstract

Spontaneous breaking of chiral symmetry in QCD has traditionally been inferred indirectly through low-energy theorems and comparison with experiments. Thanks to the understanding of an unexpected connection between chiral Random Matrix Theory and chiral Perturbation Theory, the spontaneous breaking of chiral symmetry in QCD can now be shown unequivocally from first principles and lattice simulations. In these lectures I give an introduction to the subject, starting with an elementary discussion of spontaneous breaking of global symmetries.