# Random Matrix Theory at Nonzero $\mu$ and $T$

## TL;DR

This paper reviews how random matrix theory helps understand the chiral phase transition in QCD at nonzero temperature and chemical potential, especially addressing the sign problem and eigenvalue behavior.

## Contribution

It introduces a novel perspective on the sign problem in QCD at nonzero chemical potential using random matrix theory and eigenvalue analysis.

## Key findings

- Discontinuity in chiral condensate explained without Banks-Casher relation
- Sign problem severity analyzed in microscopic QCD domain
- Eigenvalue distributions linked to phase transition behavior

## Abstract

We review applications of random matrix theory to QCD at nonzero temperature and chemical potential. The chiral phase transition of QCD and QCD-like theories is discussed in terms of eigenvalues of the Dirac operator. We show that for QCD at $\mu \ne 0$, which has a sign problem, the discontinuity in the chiral condensate is due to an alternative to the Banks-Casher relation. The severity of the sign problem is analyzed in the microscopic domain of QCD.