DescriptionThe goal of this thesis is to study the behavior of branes preserving B-type supersymmetry in two-dimensional N = (2,2) theories as parameters are varied across the (quantum-corrected) Kähler moduli space. These branes may naturally be organized into a category which is equivalent to the derived category of coherent sheaves on the target geometry. For theories constructed from an abelian gauged linear sigma model, this wall-crossing is studied using the analytic continuation of the hemisphere partition function for which an explicit integral formula is known by work on localization of Hori-Romo. This leads to an understanding of transport functors which exhibit splitting of branes between the Higgs and Coulomb branches, thus going beyond the work of Hori-Herbst-Page in the Calabi-Yau case.
As a case study, explicit brane transport is worked out for Hirzebruch-Jung surfaces, extending the work of Moore-Martinec at the level of K-theory. Furthermore, the hemisphere partition function is evaluated with suitable regularization and shown to match to leading order the known formula for central charge in terms of characteristic classes. This is based on the arXiv hep-th 1811.12385 which was joint with B. Le Floch and M. Romo.