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Nahm sums, quiver A-polynomials and topological recursion

Journal of High Energy Physics volume 2020, Article number: 151 (2020) Cite this article

A preprint version of the article is available at arXiv.

Abstract

We consider a large class of q-series that have the structure of Nahm sums, or equivalently motivic generating series for quivers. First, we initiate a systematic analysis and classification of classical and quantum A-polynomials associated to such q-series. These quantum quiver A-polynomials encode recursion relations satisfied by the above series, while classical A-polynomials encode asymptotic expansion of those series. Second, we postulate that those series, as well as their quantum quiver A-polynomials, can be reconstructed by means of the topological recursion. There is a large class of interesting quiver A-polynomials of genus zero, and for a number of them we confirm the above conjecture by explicit calculations. In view of recently found dualities, for an appropriate choice of quivers, these results have a direct interpretation in topological string theory, knot theory, counting of lattice paths, and related topics. In particular it follows, that various quantities characterizing those systems, such as motivic Donaldson-Thomas invariants, various knot invariants, etc., have the structure compatible with the topological recursion and can be reconstructed by its means.

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Authors and Affiliations

  1. Faculty of Physics, University of Warsaw, ul. Pasteura 5, 02-093, Warsaw, Poland

    Hélder Larraguível, Dmitry Noshchenko, Miłosz Panfil & Piotr Sułkowski

  2. Walter Burke Institute for Theoretical Physics, California Institute of Technology, 1200 E. California Blvd., Pasadena, CA, 91125, USA

    Piotr Sułkowski

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  1. Hélder Larraguível
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ArXiv ePrint: 2005.01776

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Larraguível, H., Noshchenko, D., Panfil, M. et al. Nahm sums, quiver A-polynomials and topological recursion. J. High Energ. Phys. 2020, 151 (2020). https://doi.org/10.1007/JHEP07(2020)151

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Keywords

  • Matrix Models
  • Topological Strings
  • Differential and Algebraic Geometry