Spectral Theories and Topological Strings on del Pezzo Geometries

Understand

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.