BPS invariants for 3-manifolds at rational level K

Abstract

We consider the Witten-Reshetikhin-Turaev invariants or Chern-Simons partition functions at or around roots of unity \( q={e}^{\frac{2\pi i}{K}} \) with a rational level K = \( \frac{r}{s} \) where r and s are coprime integers. From the exact expression for the G = SU(2) Witten-Reshetikhin-Turaev invariants of the Seifert manifolds at a rational level obtained by Lawrence and Rozansky, we provide an expected form of the structure of the Witten-Reshetikhin-Turaev invariants in terms of the homological blocks at a rational level. Also, we discuss the asymptotic expansion of knot invariants around roots of unity where we take a limit different from the limit in the standard volume conjecture.

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Correspondence to Hee-Joong Chung.

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ArXiv ePrint: 1906.12344

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Chung, HJ. BPS invariants for 3-manifolds at rational level K. J. High Energ. Phys. 2021, 83 (2021). https://doi.org/10.1007/JHEP02(2021)083

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Keywords

  • Chern-Simons Theories
  • Topological Field Theories
  • Field Theories in Lower Dimensions
  • Gauge Symmetry