Loop equations and topological recursion for the arbitrary-$\beta$ two-matrix model

We write the loop equations for the $\beta$ two-matrix model, and we propose a topological recursion algorithm to solve them, order by order in a small parameter. We find that to leading order, the spectral curve is a "quantum" spectral curve, i.e. it is given by a differential operator (i...

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Detalles Bibliográficos
Autores principales: Bergere, Michel, Eynard, Bertrand, Marchal, Olivier, Prats-Ferrer, Aleix
Lenguaje:eng
Publicado: 2011
Materias:
Mathematical Physics and Mathematics
Acceso en línea:https://dx.doi.org/10.1007/JHEP03(2012)098
http://cds.cern.ch/record/1356017
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author Bergere, Michel
Eynard, Bertrand
Marchal, Olivier
Prats-Ferrer, Aleix
author_facet Bergere, Michel
Eynard, Bertrand
Marchal, Olivier
Prats-Ferrer, Aleix
author_sort Bergere, Michel
collection CERN
description We write the loop equations for the $\beta$ two-matrix model, and we propose a topological recursion algorithm to solve them, order by order in a small parameter. We find that to leading order, the spectral curve is a "quantum" spectral curve, i.e. it is given by a differential operator (instead of an algebraic equation for the hermitian case). Here, we study the case where that quantum spectral curve is completely degenerate, it satisfies a Bethe ansatz, and the spectral curve is the Baxter TQ relation.
id cern-1356017
institution Organización Europea para la Investigación Nuclear
language eng
publishDate 2011
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spelling cern-13560172023-10-04T05:57:15Zdoi:10.1007/JHEP03(2012)098http://cds.cern.ch/record/1356017engBergere, MichelEynard, BertrandMarchal, OlivierPrats-Ferrer, AleixLoop equations and topological recursion for the arbitrary-$\beta$ two-matrix modelMathematical Physics and MathematicsWe write the loop equations for the $\beta$ two-matrix model, and we propose a topological recursion algorithm to solve them, order by order in a small parameter. We find that to leading order, the spectral curve is a "quantum" spectral curve, i.e. it is given by a differential operator (instead of an algebraic equation for the hermitian case). Here, we study the case where that quantum spectral curve is completely degenerate, it satisfies a Bethe ansatz, and the spectral curve is the Baxter TQ relation.We write the loop equations for the $\beta$ two-matrix model, and we propose a topological recursion algorithm to solve them, order by order in a small parameter. We find that to leading order, the spectral curve is a "quantum" spectral curve, i.e. it is given by a differential operator (instead of an algebraic equation for the hermitian case). Here, we study the case where that quantum spectral curve is completely degenerate, it satisfies a Bethe ansatz, and the spectral curve is the Baxter TQ relation.arXiv:1106.0332IPT-11-145CERN-2011-121IPT-11-145CERN-2011-121-[SIC!]CERN-PH-TH-2011-121oai:cds.cern.ch:13560172011-06-03
spellingShingle Mathematical Physics and Mathematics
Bergere, Michel
Eynard, Bertrand
Marchal, Olivier
Prats-Ferrer, Aleix
Loop equations and topological recursion for the arbitrary-$\beta$ two-matrix model
title Loop equations and topological recursion for the arbitrary-$\beta$ two-matrix model
title_full Loop equations and topological recursion for the arbitrary-$\beta$ two-matrix model
title_fullStr Loop equations and topological recursion for the arbitrary-$\beta$ two-matrix model
title_full_unstemmed Loop equations and topological recursion for the arbitrary-$\beta$ two-matrix model
title_short Loop equations and topological recursion for the arbitrary-$\beta$ two-matrix model
title_sort loop equations and topological recursion for the arbitrary-$\beta$ two-matrix model
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/JHEP03(2012)098
http://cds.cern.ch/record/1356017
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AT eynardbertrand loopequationsandtopologicalrecursionforthearbitrarybetatwomatrixmodel
AT marchalolivier loopequationsandtopologicalrecursionforthearbitrarybetatwomatrixmodel
AT pratsferreraleix loopequationsandtopologicalrecursionforthearbitrarybetatwomatrixmodel

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