Quantisation via Branes and Minimal Resolution
Author: Jian Qiu
Preprint number: UUITP-05/23
Abstract: The ‘brane quantisation’ procedure is developed by Gukov and Witten [GW09]. We implement this idea by combining it with the tilting theory and the minimal resolutions. This way, we can realistically compute the deformation quantisation on the space of observables acting on the Hilbert space. We apply this procedure to the quantisation problem of generalised Kähler structure on P2. Our approach differs from and complements that of Bischoff and Gualtieri [BG22]. We also benefitted from an important technical tool: a combinatorial criterion for the Maurer-Cartan equation, developed in [BW20] by Barmeier and Wang.