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Hermitian versus anti-hermitian one-matrix models and their hierarchies

Luis Miramontes, Chiara Nappi, Andrea Pasquinucci, Timothy Hollowood Orcid Logo

Nuclear Physics B, Volume: "B373", Issue: 1, Pages: 247 - 280

Swansea University Author: Timothy Hollowood Orcid Logo

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Abstract

Building on a recent work of \v C. Crnkovi\'c, M. Douglas and G. Moore, a study of multi-critical multi-cut one-matrix models and their associated $sl(2,C)$ integrable hierarchies, is further pursued. The double scaling limits of hermitian matrix models with different scaling ans\"atze, le...

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Published in: Nuclear Physics B
ISSN: 05503213
Published: 1991
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa28596
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Abstract: Building on a recent work of \v C. Crnkovi\'c, M. Douglas and G. Moore, a study of multi-critical multi-cut one-matrix models and their associated $sl(2,C)$ integrable hierarchies, is further pursued. The double scaling limits of hermitian matrix models with different scaling ans\"atze, lead, to the KdV hierarchy, to the modified KdV hierarchy and part of the non-linear Schr\"odinger hierarchy. Instead, the anti-hermitian matrix model, in the two-arc sector, results in the Zakharov-Shabat hierarchy, which contains both KdV and mKdV as reductions. For all the hierarchies, it is found that the Virasoro constraints act on the associated tau-functions. Whereas it is known that the ZS and KdV models lead to the Virasoro constraints of an $sl(2,C)$ vacuum, we find that the mKdV model leads to the Virasoro constraints of a highest weight state with arbitrary conformal
College: Faculty of Science and Engineering
Issue: 1
Start Page: 247
End Page: 280