Unitary matrix models and random partitions: Universality and multi-criticality

Abstract

The generating functions for the gauge theory observables are often represented in terms of the unitary matrix integrals. In this work, the perturbative and non-perturbative aspects of the generic multi-critical unitary matrix models are studied by adopting the integrable operator formalism, and the multi-critical generalization of the Tracy--Widom distribution in the context of random partitions. We obtain the universal results for the multi-critical model in the weak and strong coupling phases. The free energy of the instanton sector in the weak coupling regime, and the genus expansion of the free energy in the strong coupling regime are explicitly computed and the universal multi-critical phase structure of the model is explored. Finally, we apply our results in concrete examples of supersymmetric indices of gauge theories in the large $N$ limit.

49 pages, 1 figure

References in corpus (5)

• Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N=1 Dual Theories
• Counting Gauge Invariants: the Plethystic Program
• Asymptotics of Tracy-Widom distributions and the total integral of a Painlevé II function
• Blackhole/String Transition for the Small Schwarzschild Blackhole of $Ad{S}_5\times S^5$ and Critical Unitary Matrix Models
• Wilson loops in unitary matrix models at finite $N$

Cited by in corpus (7)

• All-orders asymptotics of tensor model observables from symmetries of restricted partitions
• Multicritical Schur measures and higher-order analogues of the Tracy-Widom distribution
• Interface fluctuations associated with split Fermi seas
• Gross-Witten-Wadia Phase Transition in Induced QCD on the Graph
• Classical group matrix models and universal criticality
• Universal Cusp Scaling in Random Partitions
• Asymptotics of the deformed higher order Airy-kernel determinants and applications