Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 9, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP09(2022)163
Keywords
1/N Expansion; Matrix Models
Categories
Funding
- Investissements d'Avenir program, Project ISITE-BFC [ANR-15-IDEX-0003]
- EIPHI Graduate School [ANR-17-EURE-0002]
- Bourgogne-Franche-Comte region
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We study generalizations of the Gross-Witten-Wadia unitary matrix model for the special orthogonal and symplectic groups. We show that in the large N limit, the normalized free energy is twice the value for the unitary case, and we demonstrate the universality of this result for an arbitrary number of coupling constants using generalized Cauchy identities.
We study generalizations of the Gross-Witten-Wadia unitary matrix model for the special orthogonal and symplectic groups. We show using a standard Coulomb gas treatment - employing a path integral formalism for the ungapped phase and resolvent techniques for the gapped phase with one coupling constant - that in the large N limit, the free energy normalized modulo the square of the gauge group rank is twice the value for the unitary case. Using generalized Cauchy identities for character polynomials, we then demonstrate the universality of this phase transition for an arbitrary number of coupling constants by linking this model to the random partition based on the Schur measure.
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