Spectral theories and topological strings on del Pezzo geometries

Journal of High Energy Physics

Sanefumi Moriyama¹ 

[1] Department of Physics, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi, 558-8585, Osaka, Japan;Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP), 3-3-138 Sugimoto, Sumiyoshi, 558-8585, Osaka, Japan;Osaka City University Advanced Mathematical Institute (OCAMI), 3-3-138 Sugimoto, Sumiyoshi, 558-8585, Osaka, Japan;

关键词: M-Theory;    Matrix Models;    Nonperturbative Effects;    Topological Strings;   

DOI  :  10.1007/JHEP10(2020)154

来源: Springer

【 摘 要 】

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.

【 授权许可】

CC BY