标题： 拓扑递归在双曲弦场论中的应用 显示英文标题

标题： Topological recursion for hyperbolic string field theory

摘要： 我们推导出了一种类似于米扎卡尼关于双曲弦顶点的递归关系，并研究了它对闭弦场理论的影响。 我们的构造核心在于周长体积：调和空间中区域的威尔-彼得森体积，这些区域中的元素具有周长$L \geq 0$。 只要$L \leq 2 \sinh^{-1} 1$，可以通过修改米扎卡尼的递归关系来证明这些体积满足递归关系。 通过将短裤分解应用于非规范弦振幅，我们将这种递归推广到双曲弦场理论，并证明对于任何背景，高阶顶点都可以通过迭代立方顶点来确定。 这种结构意味着闭弦场理论的解服从二次积分方程。 我们在一个被阻塞的标量理论的例子中展示了我们方法的实用性。 显示英文摘要

摘要： We derive an analog of Mirzakhani's recursion relation for hyperbolic string vertices and investigate its implications for closed string field theory. Central to our construction are systolic volumes: the Weil-Petersson volumes of regions in moduli spaces of Riemann surfaces whose elements have systoles $L \geq 0$. These volumes can be shown to satisfy a recursion relation through a modification of Mirzakhani's recursion as long as $L \leq 2 \sinh^{-1} 1$. Applying the pants decomposition of Riemann surfaces to off-shell string amplitudes, we promote this recursion to hyperbolic string field theory and demonstrate the higher order vertices are determined by the cubic vertex iteratively for any background. Such structure implies the solutions of closed string field theory obey a quadratic integral equation. We illustrate the utility of our approach in an example of a stubbed scalar theory.