# Dirac operator as a random matrix and the quenched limit of QCD with chemical potential

## TL;DR

This paper uses a random matrix approach to solve the long-standing puzzle of quenched QCD behavior at nonzero chemical potential, revealing that the quenched limit involves a theory with conjugate quarks rather than a simple replica trick.

## Contribution

It provides an explicit solution for quenched QCD at nonzero chemical potential using random matrix theory, clarifying the correct limiting procedure involving conjugate quarks.

## Key findings

- Explicit solution for quenched QCD at nonzero μ
- Naive replica trick fails in this context
- Quenched limit involves conjugate quarks with original action

## Abstract

The behavior of quenched QCD at nonzero chemical potential $\mu$ has been a long-standing puzzle. An explicit solution is found using the random matrix approach to chiral symmetry breaking. At nonzero $\mu$ the quenched QCD is not a simple $n\to0$ limit of a theory with $n$ quarks: a naive `replica trick' fails. A limit that leads to the quenched QCD is that of a theory with $2n$ quarks: $n$ quarks with original action and $n$ quarks with conjugate action.