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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.18182 |
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Table of Contents:
- We study the large-$N$ limit of $U(N)$ and $SU(N)$ unitary matrix models inspired by QCD. The model is analyzed in two cases: $μ= 0$, where the potential is real, and finite $μ$, where it becomes complex. The complex action drives the eigenvalues into the complex plane, leading to $\langle U \rangle \neq \langle U^{-1} \rangle$. In the ungapped phase, we obtain analytic expressions for the spectral density, Wilson loops, and free energy, which reproduce the low-temperature behaviour of QCD. In contrast, the gapped phase involves a nontrivial resolvent and is solved partially analytically and numerically. At $μ=0$, the model exhibits a $3^{rd}$ order phase transition, while at finite $μ$, it shows a continuous phase transition of at least second order.