Universal edge scaling in random partitions

Kimura, Taro

doi:10.1007/s11005-021-01389-y

Cited by 15 publications

(16 citation statements)

References 29 publications

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“…We remark that, as mentioned in [15], the differential/difference equation (3.14) is interpreted as a quantization of the spectral curve for the generalized GWW model,…”

Section: Jhep07(2021)100mentioning

confidence: 76%

“….) are some model-dependent parameters and are explicitly expressed in terms of the couplings [15]. The main result of our study is that the matrix model (1.1), undergoes a multi-critical phase transition at the critical point β = β c .…”

Section: Discussionmentioning

confidence: 94%

“…In this part, we review, without details of the proofs, the results obtained in recent works [15,20] about the random partitions and its asymptotics, and then adopt them to study the phase structure of gauge theories. The first step in the random partition realization of the gauge theory is to think of the random partition as discretization of the matrix integral representation of the partition function of the gauge theory.…”

Section: Integrable Operator Formalism In Matrix Modelsmentioning

confidence: 99%

“…Random partition, as a discrete analog of the random matrix [9], has similar edge scaling behavior which is reflected in terms of the probability distribution of the largest entry (the first row) of the partition. In the scaling limit, the probability distribution of the largest entry of the Schur partition is obtained in [15],…”

Section: Higher-order Tracy-widom Distributionmentioning

confidence: 99%

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

Kimura

2021

J. High Energ. Phys.

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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.

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“…We remark that, as mentioned in [15], the differential/difference equation (3.14) is interpreted as a quantization of the spectral curve for the generalized GWW model,…”

Section: Jhep07(2021)100mentioning

confidence: 76%

Section: Discussionmentioning

confidence: 94%

Section: Integrable Operator Formalism In Matrix Modelsmentioning

confidence: 99%

Section: Higher-order Tracy-widom Distributionmentioning

confidence: 99%

See 2 more Smart Citations

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

Kimura

2021

J. High Energ. Phys.

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“…and F p is the higher-order Tracy-Widom distribution [10][11][12][13], and α p (q 1 , q 2 , ...), β(q 1 , q 2 , ...) are some model-dependent parameters and are explicitly expressed in terms of the couplings [14]. The main result of our study is that the matrix model (1.1), undergoes a multi-critical phase transition at the critical point β = β c .…”

Section: Discussionmentioning

confidence: 99%

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

Kimura,

Zahabi

2021

Preprint

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The generating functions for the supersymmetric indices of the gauge theory such as superconformal index are often represented in terms of the unitary matrix integrals with double trace potential. In the limit of weak interactions between the eigenvalues, they can be approximated by the matrix models with the single-trace potential, i.e. the generalized Gross-Witten-Wadia model. 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.

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Classical group matrix models and universal criticality

Kimura

Purkayastha

2022

J. High Energ. Phys.

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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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Universal edge scaling in random partitions

Cited by 15 publications

References 29 publications

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

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

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

Classical group matrix models and universal criticality

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