论文标题
Faddeev的量子dionogarithm的复兴
Resurgence of Faddeev's quantum dilogarithm
论文作者
论文摘要
FADDEEV的量子差异功能是一种特殊的功能，它是量子Teichmüller理论和复杂Chern-Simons理论的结和3个manifolds的量子不变性的构件。以对墙壁横断现象的重新出现和最新兴趣的猜想的动机，我们证明了线性差方程的正式功率系列解决方案的Borel总和会产生FADDEEV的量子差异。一路上，我们给出了一个明确的公式，用于在Borel平面中的Meromororphic函数，定位其极点和残基，并描述其Laplace的Stokes现象沿Stokes Rays变换。
The quantum dilogarithm function of Faddeev is a special function that plays a key role as the building block of quantum invariants of knots and 3-manifolds, of quantum Teichmüller theory and of complex Chern-Simons theory. Motivated by conjectures on resurgence and recent interest in wall-crossing phenomena, we prove that the Borel summation of a formal power series solution of a linear difference equation produces Faddeev's quantum dilogarithm. Along the way, we give an explicit formula for the meromorphic function in Borel plane, locate its poles and residues, and describe the Stokes phenomenon of its Laplace transforms along the Stokes rays.
