We present a construction of an open analogue of total descendant and total ancestor potentials via an “open version” of Givental’s action. Our construction gives a genus expansion for an arbitrary solution to the open WDVV equations satisfying a semisimplicity condition and admitting a unit. We show that the open total descendant potentials we define satisfy the open topological recursion relations in genus $0$ and $1$, the open string and open dilaton equations. We finish the paper with a computation of the simplest nontrivial open correlator in genus $1$ using our construction.

中文翻译：

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全属开放后代潜能的构建

我们通过 Givental 行动的“开放版本”，展示了总后裔和总祖先潜力的开放模拟结构。我们的构造给出了满足半单性条件并允许单位的开放 WDVV 方程的任意解的属展开。我们表明，我们定义的开放总后代势满足 $0$ 和 $1$ 属中的开放拓扑递归关系、开放字符串和开放扩张子方程。我们使用我们的结构计算了 $1$ 类中最简单的非平凡开相关器来完成本文。