On D-branes from Gauged Linear Sigma Models
Suresh Govindarajan, T. Jayaraman, Tapobrata Sarkar
TL;DR
This work develops a boundary formulation of the two-dimensional N=(2,2) gauged linear sigma model to describe D-branes on Calabi–Yau threefolds with a single Kähler modulus. By deriving boundary conditions that reproduce the large-volume NLSM limit and identifying a boundary contact term required for consistency, the authors construct explicit A-type and B-type boundary data both in the GLSM and in the $e^2\to\infty$ limit, including the effects of a nonzero theta-term. They show how boundary conditions interpolate between geometric (A- and B-brane) pictures and Landau–Ginzburg phases, discuss the role of the p-field, and analyze implications for branes at the quintic Fermat point, including potential connections to Recknagel–Schomerus states and Gepner points. The paper lays groundwork for incorporating Chan–Paton data, vector bundles, and boundary superpotentials, aiming to connect open-string boundary CFT data with the GLSM description across phases. Overall, it provides a concrete worldsheet framework to study D-branes across moduli space and sets the stage for further explorations of brane superpotentials and mirror-symmetry checks via the GLSM.
Abstract
We study both A-type and B-type D-branes in the gauged linear sigma model by considering worldsheets with boundary. The boundary conditions on the matter and vector multiplet fields are first considered in the large-volume phase/non-linear sigma model limit of the corresponding Calabi-Yau manifold, where we also find that we need to add a contact term on the boundary. These considerations enable to us to derive the boundary conditions in the full gauged linear sigma model, including the addition of the appropriate boundary contact terms, such that these boundary conditions have the correct non-linear sigma model limit. Most of the analysis is for the case of Calabi-Yau manifolds with one Kahler modulus (including those corresponding to hypersurfaces in weighted projective space), though we comment on possible generalizations.