GUE via Frobenius Manifolds. II. Loop Equations

A theorem of Dubrovin establishes the relationship between the GUE partition function and the partition function of Gromov-Witten invariants of the complex projective line. Based on this theorem we derive loop equations for the Gaussian Unitary Ensemble (GUE) partition function. We show that the GUE...

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Bibliographic Details
Published inarXiv.org
Main Author Yang, Di
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 27.07.2024
Subjects
Partitions (mathematics)
Theorems
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Summary:A theorem of Dubrovin establishes the relationship between the GUE partition function and the partition function of Gromov-Witten invariants of the complex projective line. Based on this theorem we derive loop equations for the Gaussian Unitary Ensemble (GUE) partition function. We show that the GUE partition function is equal to part of the topological partition function of the non-linear Schr\"odinger (NLS) Frobenius manifold.
ISSN:2331-8422