Linear Models of Supersymmetric D-Branes
Kentaro Hori
TL;DR
The paper advances a concrete worldsheet framework for open-string D-branes in N=2 theories by constructing boundary interactions that preserve supersymmetry and feature parameters nonrenormalized beyond one loop. It develops a linear-model approach to A-type D-branes in GLSMs, including a complex chiral boundary parameter s=c-ia and a mirror LG description with quantum-deformed constraints, and extends to B-type branes via tachyon condensation. It further analyzes D0-branes in massive Landau-Ginzburg models, establishing open topological LG structure and linking these branes to Lagrangian torus branes in toric sigma models through mirror symmetry. Collectively, the work clarifies how boundary data encode brane geometry (Lagrangian/Holomorphic) and holomorphic data, yielding a robust bridge between sigma-model branes, LG branes, and their open-topological counterparts with explicit nonperturbative and quantum-corrected structures.
Abstract
We construct a class of supersymmetric boundary interactions in N=2 field theories on the half-space, which depend on parameters that are not at all renormalized or not renormalized in perturbation theory beyond one-loop. This can be used to study D-branes wrapped on a certain class of Lagrangian submanifolds as well as holomorphic cycles. The construction of holomorphic D-branes is in close relationship with the background independent open string field theory approach to brane/anti-brane systems. As an application, mirror pairs of Lagrangian and holomorphic D-branes are identified. The mirror pairs are studied by twisting to open topological field theories.