Nahm sums, quiver A-polynomials and topological recursion

Journal of High Energy Physics

Dmitry Noshchenko¹  Hélder Larraguível¹  Miłosz Panfil¹  Piotr Sułkowski² 

[1] Faculty of Physics, University of Warsaw, ul. Pasteura 5, 02-093, Warsaw, Poland;Faculty of Physics, University of Warsaw, ul. Pasteura 5, 02-093, Warsaw, Poland;Walter Burke Institute for Theoretical Physics, California Institute of Technology, 1200 E. California Blvd., 91125, Pasadena, CA, USA;

关键词: Matrix Models;    Topological Strings;    Differential and Algebraic Geometry;   

DOI  :  10.1007/JHEP07(2020)151

来源: Springer

【 摘 要 】

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.

【 授权许可】

Unknown