标题： 黑洞和三维-三维对应中的大复数瞬子$N$ 显示英文标题

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

摘要： 我们研究了从环绕超立方体的M5膜上获得的三维类 $\mathcal{R}$ 理论的扭曲指标的大 $ N$ 符号振荡。 在全息原理下，这种振荡行为可以从两个欧几里得超重力解的实部部分来理解，即带有 $p=0$ 的Bolt $_{\pm}$ 和磁荷带电的AdS $_4$ 黑洞的温克旋转。这两个解具有相反符号的相同实部。 实部来源于超重力中的 $F\wedge F$-项，系数与三维流形的Chern-Simons不变量成正比。 结合全息计算与扭曲指标的三维-三维关系，我们提出了一种关于双曲三维流形上扭曲Reidemeister-Ray-Singer扭转相位因子的非平凡数学猜想。 显示英文摘要

摘要： 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.