Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: All-order asymptotics of hyperbolic knot invariants from
  non-perturbative topological recursion of A-polynomials   We propose a conjecture to compute the all-order asymptotic expansion of the
colored Jones polynomial of the complement of a hyperbolic knot, J_N(q =
exp(2u/N)) when N goes to infinity. Our conjecture claims that the asymptotic
expansion of the colored Jones polynomial is a the formal wave function of an
integrable system whose semiclassical spectral curve S would be the SL_2(C)
character variety of the knot (the A-polynomial), and is formulated in the
framework of the topological recursion. It takes as starting point the proposal
made recently by Dijkgraaf, Fuji and Manabe (who kept only the perturbative
part of the wave function, and found some discrepancies), but it also contains
the non-perturbative parts, and solves the discrepancy problem. These
non-perturbative corrections are derivatives of Theta functions associated to
S, but the expansion is still in powers of 1/N due to the special properties of
A-polynomials. We provide a detailed check for the figure-eight knot and the
once-punctured torus bundle L^2R. We also present a heuristic argument inspired
from the case of torus knots, for which knot invariants can be computed from a
matrix model.

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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
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The categories of this paper are: econ
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The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
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The categories of this paper are: gr-qc
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The categories of this paper are: physics
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The categories of this paper are: quant-ph
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The categories of this paper are: q-alg
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The categories of this paper are: nlin