Black holes and large \(N\) complex saddles in 3D-3D correspondence. (English) Zbl 1466.83049
Summary: 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, \( \mathrm{Bolt}_\pm\) with \(p = 0\), which are Wick rotation of magnetically charged \( \mathrm{AdS}_4\) 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.
MSC:
| 83C57 | Black holes |
| 83E30 | String and superstring theories in gravitational theory |
| 83E50 | Supergravity |
| 83E05 | Geometrodynamics and the holographic principle |
| 81T60 | Supersymmetric field theories in quantum mechanics |
| 58J28 | Eta-invariants, Chern-Simons invariants |
Software:
SnapPyReferences:
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