论文标题
Del Pezzo几何形状上的光谱理论和拓扑结构
Spectral Theories and Topological Strings on del Pezzo Geometries
论文作者
论文摘要
通过理解M2-branes，我们提议通过量子曲线重新重新制定M2-branes的分区功能。尤其是，我们专注于Del Pezzo几何形状的背景，这些几何形状享有特殊代数的Weyl ofter对称性。我们明确构建量子曲线，并转向经典相空间区域和量子镜图的分析。我们发现，组结构有助于阐明以前的微妙之处，例如该区域中化学电位的转移以及镜像镜头中光谱算子的整体因子的鉴定。我们列出了表征量子镜图的多重性，并发现BPS索引已知的分离关系适用于镜像图。结果，通过组结构，我们可以明确地介绍频谱理论和拓扑几何形状之间的对应关系的陈述。
Motivated by understanding M2-branes, we propose to reformulate partition functions of M2-branes by quantum curves. Especially, we focus on the backgrounds of del Pezzo geometries, which enjoy Weyl group symmetries of exceptional algebras. We construct quantum curves explicitly and turn to the analysis of classical phase space areas and quantum mirror maps. We find that the group structure helps in clarifying previous subtleties, such as the shift of the chemical potential in the area and the identification of the overall factor of the spectral operator in the mirror map. We list the multiplicities characterizing the quantum mirror maps and find that the decoupling relation known for the BPS indices works for the mirror maps. As a result, with the group structure we can present explicitly the statement for the correspondence between spectral theories and topological strings on del Pezzo geometries.
