Black holes and Large $N$ complex saddles in 3D-3D correspondence

Abstract

We study the large $N$ sign oscillation of the twisted indices for 3D theories of class $\mathcal{R}$ 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${}_{\pm }$ 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 $F\wedge F$-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.

arXiv comment13 pages

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Cited by in corpus (3)

• Supersymmetric phases of AdS${}_4$/CFT${}_3$
• Higher-Derivative Supergravity, AdS${}_4$ Holography, and Black Holes
• Wrapped $M5$-branes and complex saddle points