Nahm sums, quiver A-polynomials and topological recursion

Nahm sums, quiver A-polynomials and topological recursion

Blog Article

Abstract We consider a large class of q-series that have the structure caramilk latte 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 teucrium cossonii majoricum 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.