Finding the Pion in the Chiral Random Matrix Vacuum

TL;DR

This paper demonstrates the existence of a Goldstone boson, specifically the pion, in chiral random matrix theory by analyzing propagators and summing phase approximations, confirming spontaneous chiral symmetry breaking.

Contribution

It provides a theoretical demonstration of the pion as a Goldstone boson within the framework of chiral random matrix theory, including calculations of effective couplings and propagators.

Findings

Confirmed the massless pion mode in the chiral random matrix vacuum

Calculated scalar and pseudoscalar propagators explicitly

Demonstrated spontaneous chiral symmetry breaking in the model

Abstract

The existence of a Goldstone boson is demonstrated in chiral random matrix theory. After determining the effective coupling and calculating the scalar and pseudoscalar propagators, a random phase approximation summation reveals the massless pion and massive sigma modes expected whenever chiral symmetry is spontaneously broken.