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Towards the continuous limit of cluster integrable systems

Franco, Sebastian; Galloni, Daniele; He, Yang-Hui

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Authors

Sebastian Franco

Daniele Galloni

Yang-Hui He



Abstract

We initiate the study of how to extend the correspondence between dimer models and (0 + 1)-dimensional cluster integrable systems to (1 + 1) and (2 + 1)-dimensional continuous integrable field theories, addressing various points that are necessary for achieving this goal. We first study how to glue and split two integrable systems, from the perspectives of the spectral curve, the resolution of the associated toric Calabi-Yau 3-folds and Higgsing in quiver theories on D3-brane probes. We identify a continuous parameter controlling the decoupling between the components and present two complementary methods for determining the dependence on this parameter of the dynamical variables of the integrable system. Interested in constructing systems with an infinite number of degrees of freedom, we study the combinatorics of integrable systems built up from a large number of elementary components, and introduce a toy model capturing important features expected to be present in a continuous reformulation of cluster integrable systems.

Citation

Franco, S., Galloni, D., & He, Y. (2012). Towards the continuous limit of cluster integrable systems. Journal of High Energy Physics, 2012(9), Article 20. https://doi.org/10.1007/jhep09%282012%29020

Journal Article Type Article
Publication Date Sep 6, 2012
Deposit Date Mar 28, 2013
Publicly Available Date Feb 7, 2014
Journal Journal of High Energy Physics
Print ISSN 1126-6708
Publisher Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Peer Reviewed Peer Reviewed
Volume 2012
Issue 9
Article Number 20
DOI https://doi.org/10.1007/jhep09%282012%29020
Keywords Brane dynamics in gauge theories, Conformal field models in string theory, Integrable equations in physics.

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Publisher Licence URL
http://creativecommons.org/licenses/by/4.0/

Copyright Statement
Open Access. This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.





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