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The resurgent structure of quantum knot invariants

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arxiv 2007.10190 v2 pith:XHWC6ZTM submitted 2020-07-20 hep-th math.GT

The resurgent structure of quantum knot invariants

Stavros Garoufalidis , Jie Gu , Marcos Marino This is my paper
classification hep-th math.GT
keywords knotseriesconjectureexplicitlygiveninvariantsmatricespair
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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The asymptotic expansion of quantum knot invariants in complex Chern-Simons theory gives rise to factorially divergent formal power series. We conjecture that these series are resurgent functions whose Stokes automorphism is given by a pair of matrices of $q$-series with integer coefficients, which are determined explicitly by the fundamental solutions of a pair of linear $q$-difference equations. We further conjecture that for a hyperbolic knot, a distinguished entry of those matrices equals to the Dimofte-Gaiotto-Gukov 3D-index, and thus is given by a counting of BPS states. We illustrate our conjectures explicitly by matching theoretically and numerically computed integers for the cases of the $4_1$ and the $5_2$ knots.

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Cited by 3 Pith papers

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