Nahm sums, quiver A-polynomials and topological recursion

Nahm sums, quiver A-polynomials and topological recursion

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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 kenya tree coral for sale 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 catherine lansfield ombre rainbow clouds eyelet curtains 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.