Linear Sigma Models for Open Strings
Simeon Hellerman, Shamit Kachru, Albion Lawrence, John McGreevy
TL;DR
The paper develops a framework of massive ${ m N}=2$ boundary GLSMs to describe open strings ending on D-branes in Calabi–Yau backgrounds, with the infrared physics realizing open-string sigma models in both large-radius and non-geometric phases (e.g., LG orbifolds). It encodes D-brane data via boundary degrees of freedom and a boundary superpotential that preserves B-type supersymmetry, enabling explicit computation of brane spectra, monodromies, and marginal-stability phenomena through RG-invariant boundary couplings. Intersections and unions of branes are realized through boundary superpotentials, tensor-product resolutions, and sheafy-variable formulations, providing a unified, calculable description of brane moduli and transitions such as Higgs–Coulomb and brane recombination. The approach yields concrete tools for analyzing brane monodromies, singularities in open-string moduli, and the spectrum of massless boundary states, across phases including the quintic in large-radius, Gepner, and LG limits. Overall, the work bridges geometric and nongeometric brane descriptions and offers a path to computing open-string data directly from a worldsheet linear model.
Abstract
We formulate and study a class of massive N=2 supersymmetric gauge field theories coupled to boundary degrees of freedom on the strip. For some values of the parameters, the infrared limits of these theories can be interpreted as open string sigma models describing D-branes in large-radius Calabi-Yau compactifications. For other values of the parameters, these theories flow to CFTs describing branes in more exotic, non-geometric phases of the Calabi-Yau moduli space such as the Landau-Ginzburg orbifold phase. Some simple properties of the branes (like large radius monodromies and spectra of worldvolume excitations) can be computed in our model. We also provide simple worldsheet models of the transitions which occur at loci of marginal stability, and of Higgs-Coulomb transitions.