Abstract
In this work we attempt to bridge the gap between heterotic orbifold models and Calabi‐Yau compactifications using gauged linear sigma models (GLSMs) with (2,0) worldsheet supersymmetry. We associate a specific GLSM to a heterotic orbifold model with twisted states that have non‐vanishing vacuum expectation values (VEVs): The charges of the GLSM superfields are essentially determined by the shifted momenta of these states. When a twisted state contains an oscillator excitation, a fermionic gauging is introduced on the worldsheet, inducing a non‐Abelian gauge bundle, e.g. the standard embedding. However, irrespectively of whether the twisted states contain oscillators or not, they can be interpreted as blow‐up modes, as their VEVs are correlated with sizes of exceptional cycles in the resolved geometry. We show that the GLSM anomaly cancellation conditions ensure that the Bianchi identities are fulfilled for all possible triangulations of a resolution. By considering marginal deformations of a GLSM in the large volume limit we are able to directly determine its effective four dimensional spectrum. In the cases considered the spectra coincide with those computed via index theorems.