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

Gang, Dongmin; Romo, Mauricio; Yamazaki, Masahito

doi:10.1007/s00220-018-3115-y

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

Journal Article · Fri Mar 16 00:00:00 EDT 2018 · Communications in Mathematical Physics

DOI:https://doi.org/10.1007/s00220-018-3115-y· OSTI ID:1537662

Gang, Dongmin ^[1]; Romo, Mauricio ^[2]; Yamazaki, Masahito ^[1]

Univ. of Tokyo (Japan). Kavli Inst. for the Physics and Mathematics of the Universe (IPMU)
Inst. for Advanced Study, Princeton, NJ (United States). School of Natural Sciences

In this paper, 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 at 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 $$q = e<^{2πi/r}$$ with $$r$$ odd, in the limit $r → ∞$. We provide numerical evidence for our conjecture.

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Research Organization:: Institute for Advanced Study, Princeton, NJ (United States)

Sponsoring Organization:: USDOE Office of Science (SC); Ministry of Education, Culture, Sports, Science and Technology (MEXT) (Japan); Japan Society for the Promotion of Science (JSPS); National Research Foundation of Korea (NRF)

Grant/Contract Number:: SC0009988; 15K17634

OSTI ID:: 1537662

Report Number(s):: arXiv:1704.00918v2; PII: 3115

Journal Information:: Communications in Mathematical Physics, Vol. 359, Issue 3; ISSN 0010-3616

Publisher:: SpringerCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 13 works

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Symmetry enhancement and closing of knots in 3d/3d correspondence Gang, Dongmin; Yonekura, Kazuya arXiv https://doi.org/10.48550/arxiv.1803.04009	text	January 2018

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