论文标题
转移的Witten课程和拓扑递归
Shifted Witten classes and topological recursion
论文作者
论文摘要
witten $ r $ - Spin类定义了一个非偏simimple的共同体学场理论。 Pandharipande，Pixton和Zvonkine使用Givental-Teleman重建定理研究了Witten类的两个特殊转变。我们表明，$ r $ -matrix和这两个特定偏移的翻译可以从两个微分方程的解决方案构建，这些方程将经典的通风微分方程推广。使用此过程，我们证明了转移的Witten类的后代交点理论满足了两个$ 1 $ - 参数曲线的拓扑递归。通过对这些光谱曲线族的参数限制为零，我们证明可以通过拓扑递归计算$ r $ $ r $ airy光谱曲线的后代相交理论。我们最终证明，这一证明足以推断出Witten的$ R $ -SPIN猜想，该猜想已经由Faber，Shadrin和Zvonkine证明，该猜想声称$ R $ -SPIN相交数字的生成系列是满足字符串方程的$ R $ -KDV HierateRARCE的TAU函数。
The Witten $r$-spin class defines a non-semisimple cohomological field theory. Pandharipande, Pixton and Zvonkine studied two special shifts of the Witten class along two semisimple directions of the associated Dubrovin--Frobenius manifold using the Givental--Teleman reconstruction theorem. We show that the $R$-matrix and the translation of these two specific shifts can be constructed from the solutions of two differential equations that generalise the classical Airy differential equation. Using this, we prove that the descendant intersection theory of the shifted Witten classes satisfies topological recursion on two $1$-parameter families of spectral curves. By taking the limit as the parameter goes to zero for these families of spectral curves, we prove that the descendant intersection theory of the Witten $r$-spin class can be computed by topological recursion on the $r$-Airy spectral curve. We finally show that this proof suffices to deduce Witten's $r$-spin conjecture, already proved by Faber, Shadrin and Zvonkine, which claims that the generating series of $r$-spin intersection numbers is the tau function of the $r$-KdV hierarchy that satisfies the string equation.
