All-Order Volume Conjecture for Closed 3-Manifolds from Complex Chern-Simons Theory

2017/04/04 by Dongmin Gang, Mauricio Romo, Masahito Yamazaki · 1 voice
Mathematics · Physics and Astronomy · #hep-th #math-ph #math.GT #math.MP #math.QA

paper · pdf · doi:10.1007/s00220-018-3115-y

published as Commun. Math. Phys. 359, 915-936 (2018) · 22 pages, 2 figures; v2: published version

arxiv published 2017/04/04 · arxiv created 2018/09/12 · arxiv updated 2018/09/14

Abstract

We propose an extension of the recently-proposed volume conjecture for closed hyperbolic 3-manifolds, to all orders in perturbative expansion. We first derive formulas for the perturbative expansion of the partition function of complex Chern-Simons theory around a hyperbolic flat connection, which produces infinitely-many perturbative invariants of the closed oriented 3-manifold. The conjecture is that this expansion coincides with the perturbative expansion of the Witten-Reshetikhin-Turaev invariants at roots of unity q=e^{2 πi/r} with r odd, in the limit r → ∞. We provide numerical evidence for our conjecture.

Discussions

• Submitted a new paper on volume conjecture, with Dongmin and Mauricio! http://arxiv.org/abs/1704.00918 体積予想の論文は実は初めて，数値計算もできるので僕らの予想をチェックしてみて下さい． [bsky, 0 points, 0 comments]

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