Non-geometric Calabi-Yau compactifications and fractional mirror symmetry

TL;DR

This paper introduces a broad class of non-geometric string compactifications that extend mirror symmetry to include quantum equivalences between Calabi-Yau and non-Calabi-Yau spaces, involving novel Landau-Ginzburg models.

Contribution

It constructs non-geometric Calabi-Yau compactifications with N=1 supersymmetry and generalizes mirror symmetry through quantum equivalences involving complex Landau-Ginzburg models.

Findings

Established non-geometric compactifications preserving supersymmetry.

Demonstrated quantum equivalences between Calabi-Yau and non-Calabi-Yau spaces.

Developed Landau-Ginzburg models with chiral and twisted chiral multiplets.

Abstract

We construct a wide class of non-geometric compactifications of type II superstring theories preserving N=1 space-time supersymmetry in four dimensions, starting from Calabi-Yau compactifications at Gepner points. Particular examples of this construction provide quantum equivalences between Calabi-Yau compactifications and non-Calabi-Yau ones, generalizing mirror symmetry. The associated Landau-Ginzburg models involve both chiral and twisted chiral multiplets hence cannot be lifted to ordinary Calabi-Yau gauged linear sigma-models.