Dual Pairs of Gauged Linear Sigma Models and Derived Equivalences of Calabi-Yau threefolds

Understand

In this work we study the phase structure of skew symplectic sigma models, which are a certain class of two-dimensional N = (2,2) non-Abelian gauged linear sigma models.

• At low energies some of them flow to non-linear sigma models with Calabi-Yau target spaces, which emerge from non-Abelian strong coupling dynamics.
• The observed phase structure results in a non-trivial duality proposal among skew symplectic sigma models and connects non-complete intersection Calabi-Yau threefolds, that are non-birational among another, in a common quantum Kahler moduli space.
• As a consequence we find non-trivial identifications of spectra of topological B-branes, which from a modern algebraic geometry perspective imply derived equivalences among Calabi-Yau varieties.