Rotational Symmetry Breaking in Multi-Matrix Models

TL;DR

This paper investigates whether O(D) symmetry in multi-matrix models is spontaneously broken at large N, revealing a phase diagram with a critical boundary where maximal symmetry breaking occurs.

Contribution

It introduces a class of multi-matrix models with O(D) invariance and analyzes their phase structure, identifying conditions for spontaneous symmetry breaking.

Findings

Existence of a critical boundary for symmetry breaking.

Maximal symmetry breaking occurs at the critical boundary.

Phase diagram characterizes symmetry behavior at large N.

Abstract

We consider a class of multi-matrix models with an action which is O(D) invariant, where D is the number of NxN Hermitian matrices X_\mu, \mu=1,...,D. The action is a function of all the elementary symmetric functions of the matrix $T_{\mu\nu}=Tr(X_\mu X_\nu)/N$. We address the issue whether the O(D) symmetry is spontaneously broken when the size N of the matrices goes to infinity. The phase diagram in the space of the parameters of the model reveals the existence of a critical boundary where the O(D) symmetry is maximally broken.