论文标题
拓扑递归和未耦合的BPS结构I：BPS频谱和自由能
Topological recursion and uncoupled BPS structures I: BPS spectrum and free energies
论文作者
论文摘要
对于高几何频谱曲线及其汇合变性（“高几幅类型”的光谱曲线），我们获得了一个简单的公式，该公式表达拓扑递归的自由能作为BPS状态（退化光谱网络）的总和，用于相应的四边形微分$φ$。在此过程中，我们概括了Gaiotto-Moore-Neitzke的BPS结构的结构，包括$φ$具有简单杆或支持退化环域的情况。对于超几何类型的九个光谱曲线，我们在相关参数空间中的通用基因座上提供了相应的BPS结构的完整描述；特别是，我们证明了在预期参数值下的马鞍轨迹的存在。我们确定相应的BPS循环，中央电荷和BPS不变性，并在每种情况下验证我们的公式。我们猜想，只要与相应的BPS结构取消耦合，相似的关系应更加普遍地保持，并在两个简单的高级示例中提供实验证据。
For the hypergeometric spectral curve and its confluent degenerations (spectral curves of "hypergeometric type"), we obtain a simple formula expressing the topological recursion free energies as a sum over BPS states (degenerate spectral networks) for a corresponding quadratic differential $φ$. In doing so, we generalize Gaiotto-Moore-Neitzke's construction of BPS structures to include the case where $φ$ has simple poles or supports a degenerate ring domain. For the nine spectral curves of hypergeometric type, we provide a complete description of the corresponding BPS structures over a generic locus in the relevant parameter space; in particular, we prove the existence of saddles trajectories at the expected parameter values. We determine the corresponding BPS cycles, central charges, and BPS invariants, and verify our formula in each case. We conjecture that a similar relation should hold more generally whenever the corresponding BPS structure is uncoupled, and provide experimental evidence in two simple higher rank examples.
