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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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DOI (Published version): 10.1016/0550-3213(92)90457-M

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
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URI: https://cronfa.swan.ac.uk/Record/cronfa28596
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first_indexed 2016-06-03T19:16:36Z
last_indexed 2018-02-09T05:12:54Z
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spelling 2016-06-03T14:37:09.0952029 v2 28596 2016-06-03 Hermitian versus anti-hermitian one-matrix models and their hierarchies ea9ca59fc948276ff2ab547e91bdf0c2 0000-0002-3258-320X Timothy Hollowood Timothy Hollowood true false 2016-06-03 SPH 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 Journal Article Nuclear Physics B "B373" 1 247 280 05503213 30 9 1991 1991-09-30 10.1016/0550-3213(92)90457-M http://inspirehep.net/record/318729 COLLEGE NANME Physics COLLEGE CODE SPH Swansea University 2016-06-03T14:37:09.0952029 2016-06-03T14:37:08.8612014 Faculty of Science and Engineering School of Biosciences, Geography and Physics - Physics Luis Miramontes 1 Chiara Nappi 2 Andrea Pasquinucci 3 Timothy Hollowood 0000-0002-3258-320X 4
title Hermitian versus anti-hermitian one-matrix models and their hierarchies
spellingShingle Hermitian versus anti-hermitian one-matrix models and their hierarchies
Timothy Hollowood
title_short Hermitian versus anti-hermitian one-matrix models and their hierarchies
title_full Hermitian versus anti-hermitian one-matrix models and their hierarchies
title_fullStr Hermitian versus anti-hermitian one-matrix models and their hierarchies
title_full_unstemmed Hermitian versus anti-hermitian one-matrix models and their hierarchies
title_sort Hermitian versus anti-hermitian one-matrix models and their hierarchies
author_id_str_mv ea9ca59fc948276ff2ab547e91bdf0c2
author_id_fullname_str_mv ea9ca59fc948276ff2ab547e91bdf0c2_***_Timothy Hollowood
author Timothy Hollowood
author2 Luis Miramontes
Chiara Nappi
Andrea Pasquinucci
Timothy Hollowood
format Journal article
container_title Nuclear Physics B
container_volume "B373"
container_issue 1
container_start_page 247
publishDate 1991
institution Swansea University
issn 05503213
doi_str_mv 10.1016/0550-3213(92)90457-M
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Biosciences, Geography and Physics - Physics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Biosciences, Geography and Physics - Physics
url http://inspirehep.net/record/318729
document_store_str 0
active_str 0
description 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
published_date 1991-09-30T03:34:51Z
_version_ 1763751484509388800
score 11.036706

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