Quantum integrability from non-simply laced quiver gauge theory

Journal of High Energy Physics, Jun 2018

Abstract We consider the compactifcation of 5d non-simply laced fractional quiver gauge theory constructed in [1]. In contrast to the simply laced quivers, here two Ω-background parameters play different roles, so that we can take two possible Nekrasov-Shatashvili limits. We demonstrate how different quantum integrable systems can emerge from these two limits, using BC2-quiver as the simplest illustrative example for our general results. We also comment possible connections with compactified 3d non-simply laced quiver gauge theory.

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Quantum integrability from non-simply laced quiver gauge theory

Journal of High Energy Physics June 2018, 2018:165 | Cite as Quantum integrability from non-simply laced quiver gauge theory AuthorsAuthors and affiliations Heng-Yu ChenTaro Kimura Open Access Regular Article - Theoretical Physics First Online: 28 June 2018 Received: 13 May 2018 Accepted: 24 June 2018 Abstract We consider the compactifcation of 5d non-simply laced fractional quiver gauge theory constructed in [1]. In contrast to the simply laced quivers, here two Ω-background parameters play different roles, so that we can take two possible Nekrasov-Shatashvili limits. We demonstrate how different quantum integrable systems can emerge from these two limits, using BC2-quiver as the simplest illustrative example for our general results. We also comment possible connections with compactified 3d non-simply laced quiver gauge theory. Keywords Bethe Ansatz Supersymmetric Gauge Theory Duality in Gauge Field Theories Integrable Field Theories  ArXiv ePrint: 1805.01308 Download to read the full article text Notes Open Access This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. References [1] T. Kimura and V. Pestun, Fractional quiver W-algebras, arXiv:1705.04410 [INSPIRE]. [2] A. Gorsky et al., Integrability and Seiberg-Witten exact solution, Phys. Lett. B 355 (1995) 466 [hep-th/9505035] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar [3] E.J. Martinec and N.P. Warner, Integrable systems and supersymmetric gauge theory, Nucl. Phys. B 459 (1996) 97 [hep-th/9509161] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar [4] R. Donagi and E. Witten, Supersymmetric Yang-Mills theory and integrable systems, Nucl. Phys. 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Heng-Yu Chen, Taro Kimura. Quantum integrability from non-simply laced quiver gauge theory, Journal of High Energy Physics, 2018, 165, DOI: 10.1007/JHEP06(2018)165