Journal
COMMUNICATIONS IN MATHEMATICAL PHYSICS
Volume 359, Issue 3, Pages 915-936Publisher
SPRINGER
DOI: 10.1007/s00220-018-3115-y
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Funding
- WPI program (MEXT, Japan)
- JSPS-NRF Joint Research Project
- JSPS Program for Advancing Strategic International Networks
- JSPS KAKENHI [15K17634]
- Institute for Advanced Study, DOE [DE-SC0009988]
- Adler Family Fund
- Grants-in-Aid for Scientific Research [15K17634] Funding Source: KAKEN
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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 with r odd, in the limit . We provide numerical evidence for our conjecture.
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