论文标题
2D拓扑重力中开放自由能的扩展属
Genus expansion of open free energy in 2d topological gravity
论文作者
论文摘要
我们研究了二维的开放拓扑重力，或者是由Pandharipande，Solomon和Tessler发起的开放式Riemann表面模量空间的相交理论。开放的自由能，开放交叉数的生成函数，遵守开放的KDV方程和Buryak的微分方程，并通过正式的傅立叶变换到KDV层次结构的Baker-Akhiezer波函数相关。使用这些特性，我们详细研究了自由能的属扩展。我们明确构建自由能的零部分。然后，我们通过求解Buryak的方程来制定一种计算较高属校正的方法，并使它们达到高阶。基于鞍点计算，此方法比我们以前的方法更有效。在途中，我们表明较高的属校正是变量中的多项式，这些变量仅以零属的属性表示，从而推广了封闭拓扑引力的构成关系。
We study open topological gravity in two dimensions, or, the intersection theory on the moduli space of open Riemann surfaces initiated by Pandharipande, Solomon and Tessler. The open free energy, the generating function for the open intersection numbers, obeys the open KdV equations and Buryak's differential equation and is related by a formal Fourier transformation to the Baker-Akhiezer wave function of the KdV hierarchy. Using these properties we study the genus expansion of the free energy in detail. We construct explicitly the genus zero part of the free energy. We then formulate a method of computing higher genus corrections by solving Buryak's equation and obtain them up to high order. This method is much more efficient than our previous approach based on the saddle point calculation. Along the way we show that the higher genus corrections are polynomials in variables that are expressed in terms of genus zero quantities only, generalizing the constitutive relation of closed topological gravity.
