B-brane transport in anomalous (2,2) models and localization

We study how B-branes in two-dimensional N=(2,2) anomalous models behave as we vary the energy scale and bulk parameters in the quantum K\"ahler moduli space. We focus on (2,2) theories defined by abelian gauged linear sigma models (GLSM). Guided by the hemisphere partition function we find how B-branes split in arbitrary phases into components on the Higgs branch and other branches: this generalizes the band restriction rules of Herbst-Hori-Page to (abelian) anomalous models. Secondly, we address divergences in non-compact models, through the central example of GLSMs for Hirzebruch-Jung resolutions of cyclic surface singularities. For a brane with compact support we explain how to regularize and compute the hemisphere partition function and extract its Higgs branch component, which we match in the zero-instanton sector to the geometric central charge of the brane. To this aim, we clarify the definition of zero-instanton geometric central charge for objects in the derived category of a non-compact toric orbifold.