Heterotic orbifold resolutions as (2,0) gauged linear sigma models

TL;DR

This paper develops a framework linking heterotic orbifold models to Calabi-Yau compactifications through (2,0) GLSMs, enabling direct computation of four-dimensional spectra consistent with index theorem results.

Contribution

It introduces a novel approach using (2,0) GLSMs to connect heterotic orbifolds with geometric resolutions, incorporating twisted states and their VEVs into the model.

Findings

GLSM charges determined by shifted momenta of twisted states

Fermionic gaugings induce non-Abelian gauge bundles

Computed spectra match index theorem predictions

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. 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.