Communications in Mathematical Physics

, Volume 359, Issue 3, pp 915–936 | Cite as

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

  • Dongmin Gang
  • Mauricio Romo
  • Masahito Yamazaki


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 \({q=e^{2\pi i/r}}\) with r odd, in the limit \({r\to \infty}\). We provide numerical evidence for our conjecture.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Dongmin Gang
    • 1
  • Mauricio Romo
    • 2
  • Masahito Yamazaki
    • 1
  1. 1.Kavli IPMUUniversity of TokyoKashiwaJapan
  2. 2.School of Natural SciencesInstitute for Advanced StudyPrincetonUSA

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