Nahm sums, quiver A-polynomials and topological recursion

A bstract 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-polyno...

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Published in:The journal of high energy physics Vol. 2020; no. 7; pp. 1 - 52
Main Authors: Larraguível, Hélder, Noshchenko, Dmitry, Panfil, Miłosz, Sułkowski, Piotr
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2020
Springer Nature B.V
SpringerOpen
Subjects:
Asymptotic series
Classical and Quantum Gravitation
Differential and Algebraic Geometry
Elementary Particles
High energy physics
Invariants
Knot theory
Matrix Models
Physics
Physics and Astronomy
Polynomials
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
String Theory
Sums
Topological Strings
Topology
Topological Strings
Matrix Models
Differential and Algebraic Geometry
ISSN:1029-8479, 1029-8479
Online Access:Get full text
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Summary:A bstract 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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ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP07(2020)151