Advances in Theoretical and Mathematical Physics

Volume 25 (2021)

Number 7

Adjoint Reidemeister torsions from wrapped M5-branes

Pages: 1819 – 1845



Dongmin Gang (Department of Physics and Astronomy & Center for Theoretical Physics, Seoul National University, Seoul, South Korea)

Seonhwa Kim (Department of Mathematics, University of Seoul, South Korea)

Seokbeom Yoon (International Center for Mathematics, Department of Mathematics, Southern University of Science and Technology, Shenzhen, China)


We introduce a vanishing property of the adjoint Reidemeister torsion of a cusped hyperbolic $3$-manifold derived from the physics of wrapped M5-branes on the manifold. To support our physical observation, we present a rigorous proof for the figure-eight knot complement with respect to all slopes. We also present numerical verification for several knots.

The research of D.G. were supported in part by the National Research Foundation of Korea (NRF) grant 2019R1A2C-2004880. The work of S.K. was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2019R1C1C1003383). S.Y. was supported by Basic Science Research Program through the NRF of Korea funded by the Ministry of Education (2020R1A6A3A03037901).

Published 11 July 2022