BPS spectra and algebraic solutions of discrete integrable systems

Abstract

This paper extends the correspondence between discrete Cluster Integrable Systems and BPS spectra of five-dimensional N = 1 QFTs on R4 × S1 by proving that algebraic solutions of the integrable systems are exact solutions for the system of TBA equations arising from the BPS spectral problem. This statement is exemplified in the case of M-theory compactifications on local del Pezzo Calabi–Yau threefolds, corresponding to q-Painlevé equations and SU(2) gauge theories with matter. A degeneration scheme is introduced, allowing to obtain closed-form expression for the BPS spectrum also in systems without algebraic solutions. By studying the example of local del Pezzo 3, it is shown that when the region in moduli space associated to an algebraic solution is a “wall of marginal stability”, the BPS spectrum contains states of arbitrarily high spin, and corresponds to a 5d uplift of a four-dimensional nonlagrangian theory.

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Item Type:	Article
Authors/Creators:	Del Monte, F. https://orcid.org/0000-0003-3367-8873
Copyright, Publisher and Additional Information:	© The Author(s) 2024. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Dates:	Published: June 2024 Published (online): 28 May 2024 Accepted: 16 April 2024
Institution:	The University of Sheffield
Academic Units:	The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield)
Depositing User:	Symplectic Sheffield
Date Deposited:	04 Jun 2024 14:16
Last Modified:	04 Jun 2024 14:16
Published Version:	http://dx.doi.org/10.1007/s00220-024-05016-4
Status:	Published
Publisher:	Springer Science and Business Media LLC
Refereed:	Yes
Identification Number:	10.1007/s00220-024-05016-4
Open Archives Initiative ID (OAI ID):	oai:eprints.whiterose.ac.uk:213055

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BPS spectra and algebraic solutions of discrete integrable systems

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