Black holes and large N complex saddles in 3D-3D correspondence

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 AdS(4) black holes. The two solutions have the same imaginary part with opposite sign. The imaginary part comes from the F boolean AND 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.

Automated summary

In this study, the large N sign oscillation of twisted indices for 3D theories on hyperbolic 3-manifolds obtained from M5-branes was investigated. The oscillatory behavior was understood holographically in terms of on-shell actions for Euclidean supergravity solutions, revealing a mathematical conjecture about the phase factor of a twisted Reidemeister-Ray-Singer torsion on hyperbolic 3-manifolds through the 3D-3D relation.