Elliptic Genera of 2d (0,2) Gauge Theories from Brane Brick Models

Understand

We compute the elliptic genus of abelian 2d (0,2) gauge theories corresponding to brane brick models.

• These theories are worldvolume theories on a single D1-brane probing a toric Calabi-Yau 4-fold singularity.
• We identify a match with the elliptic genus of the non-linear sigma model on the same Calabi-Yau background, which is computed using a new localization formula.
• The matching implies that the quantum effects do not drastically alter the correspondence between the geometry and the 2d (0,2) gauge theory.