Abstract
We study the large N sign oscillation of the twisted indices for 3D theories of class ℛ obtained from M5-branes wrapped on a hyperbolic 3-manifold. Holographically, the oscillatory behavior can be understood from the imaginary part of on-shell actions for the two Euclidean supergravity solutions, Bolt± with p = 0, which are Wick rotation of magnetically charged AdS4 black holes. The two solutions have the same imaginary part with opposite sign. The imaginary part comes from the F ∧ F-term in the supergravity and the coefficient is proportional to the Chern-Simons invariant of 3-manifold. Combining the holographic computation with 3D-3D relation for twisted indices, we propose a non-trivial mathematical conjecture regarding the phase factor of a twisted Reidemeister-Ray-Singer torsion on hyperbolic 3-manifold.
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Choi, S., Gang, D. & Kim, N. Black holes and large N complex saddles in 3D-3D correspondence. J. High Energ. Phys. 2021, 78 (2021). https://doi.org/10.1007/JHEP06(2021)078
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DOI: https://doi.org/10.1007/JHEP06(2021)078