Abstract
In a generalized Airy matrix model, a power p replaces the cubic term of the Airy model introduced by Kontsevich. The parameter p corresponds to Witten’s spin index in the theory of intersection numbers of moduli space of curves. A continuation in p down to p = −2 yields a well studied unitary matrix model. The application of duality and replica to the p-th Airy model provides, through this equivalence, a generating function for both the weak and the strong coupling expansions of the unitary model. We thereby recover and extend further the results for these expansions.
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ArXiv ePrint: 1005.4730
France: Unité Mixte de Recherche 8549 du Centre National de la Recherche Scientifique et de l’ Ecole Normale Supérieure.
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Brézin, E., Hikami, S. Duality and replicas for a unitary matrix model. J. High Energ. Phys. 2010, 67 (2010). https://doi.org/10.1007/JHEP07(2010)067
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DOI: https://doi.org/10.1007/JHEP07(2010)067