Ẑ invariants at rational τ

Creators: Kucharski, Piotr

Abstract

Ẑ invariants of 3-manifolds were introduced as series in q = e^(2πiτ) in order to categorify Witten-Reshetikhin-Turaev invariants corresponding to τ = 1/k. However modularity properties suggest that all roots of unity are on the same footing. The main result of this paper is the expression connecting Reshetikhin-Turaev invariants with Ẑ invariants for τ ∈ ℚ. We present the reasoning leading to this conjecture and test it on various 3-manifolds.

Additional Information

© 2019 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP3. Received: July 23, 2019; Accepted: August 24, 2019; Published: September 12, 2019. I would like to thank Sergei Gukov for his mentoring, Sungbong Chun for invaluable support, and Miranda Cheng for directing my attention to this topic. I am also grateful to Francesca Ferrari, Sarah Harrison, Thang Le, Pavel Putrov, and Piotr Su lkowski for insightful discussions. My work is supported by the Polish Ministry of Science and Higher Education through its programme Mobility Plus (decision no. 1667/MOB/V/2017/0). This research was supported in part by the National Science Foundation under Grant No. NSF PHY-1748958 while I was visiting Kavli Institute for Theoretical Physics in Santa Barbara.

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Submitted - 1906.09768.pdf

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