# Random matrix model of QCD at finite density and the nature of the quenched limit

## TL;DR

This paper employs a random matrix model to analyze chiral symmetry breaking in QCD at finite chemical potential, revealing that quenched QCD corresponds to a theory with doubled quark flavors rather than a straightforward limit, and aligning with lattice QCD findings.

## Contribution

It demonstrates that quenched QCD at finite density is equivalent to a theory with twice the number of quarks, clarifying a long-standing puzzle and providing an analytical framework.

## Key findings

- Quenched QCD is not a simple $n o0$ limit of QCD with $n$ quarks.
- The eigenvalue density of the Dirac matrix is computed on a complex plane.
- Results agree with lattice QCD studies at finite chemical potential.

## Abstract

We use a random matrix model to study chiral symmetry breaking in QCD at finite chemical potential $\mu$. We solve the model and compute the eigenvalue density of the Dirac matrix on a complex plane. A naive ``replica trick'' fails for $\mu\neq0$: we find that quenched QCD is not a simple $n\to0$ limit of QCD with $n$ quarks. It is the limit of a theory with $2n$ quarks: $n$ quarks with original action and $n$ quarks with conjugate action. The results agree with earlier studies of lattice QCD at $\mu\neq0$ and provide a simple analytical explanation of a long-standing puzzle.