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We report on recent progress in heterotic string compactific ations using gauged linear sigma models (GLSMs). (2,0) GLSMs are proposed to smoothly interpolate between non‐compact heterotic orbifold models and large volume Calabi‐Yau compactificati ons. The charges of these GLSMs are determined from the shifted momenta that characterize the twisted states that take VEVs which generate the blow‐up. To allow for more flexibility to o btain solutions to the worldsheet anomaly cancellation conditions, we consider a worldsheet version of the Green‐Schwarz mechanism involving field dependent Fayet‐Iliopoulos terms.

Green-Schwarz mechanism in heterotic 2,0 gauged linear sigma models