论文标题
3D-3D通信中的黑洞和大$ N $复杂的马鞍
Black holes and Large $N$ complex saddles in 3D-3D correspondence
论文作者
论文摘要
我们研究了从包裹在双曲线3个manifold上的M5-Branes获得的类$ \ Mathcal {r} $ 3D理论的扭曲指数的大$ n $标志振荡。从全息方面，可以从两个欧几里得超级实力解决方案的壳体动作的虚构部分中理解振荡行为，螺栓$ _ {\ pm} $，$ p = 0 $，这是磁性电荷的wick旋转磁性电荷的广告$ _4 $ _4 $ _4 $黑孔。这两种解决方案具有相同的假想部分，具有相反的符号。假想的部分来自超级重力的$ f \ wedge f $ - 术语，系数与3个manifold的Chern-Simons成正比。将全息计算与扭曲指数的3D-3D关系相结合，我们提出了一个非平凡的数学猜想，内容涉及双曲线3个manifold上扭曲的reidemeister-ray-serger扭转的相位因子。
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.
