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Journal of High Energy Physics

, 2019:92 | Cite as

invariants at rational τ

  • Piotr KucharskiEmail author
Open Access
Regular Article - Theoretical Physics
  • 37 Downloads

Abstract

invariants of 3-manifolds were introduced as series in q = e2πiτ 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 invariants for τ. We present the reasoning leading to this conjecture and test it on various 3-manifolds.

Keywords

Chern-Simons Theories Quantum Groups Supersymmetric Gauge Theory Topological Field Theories 

Notes

Open Access

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.

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Walter Burke Institute for Theoretical Physics, California Institute of TechnologyPasadenaU.S.A.
  2. 2.Faculty of PhysicsUniversity of WarsawWarsawPoland

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