Brane Brick Models and 2d (0,2) Triality

TL;DR

This paper introduces a brane-based realization of 2d (0,2) triality using brane brick models, demonstrating their transformations, invariance of moduli space, and connections to Calabi-Yau 4-folds.

Contribution

It provides the first brane construction of 2d (0,2) triality via brane brick models and explores their properties and invariances.

Findings

Triality corresponds to cube moves in brane brick models.

The classical mesonic moduli space remains invariant under triality.

Phase boundaries are key to connecting Calabi-Yau 4-folds with brane brick models.

Abstract

We provide a brane realization of 2d (0,2) Gadde-Gukov-Putrov triality in terms of brane brick models. These are Type IIA brane configurations that are T-dual to D1-branes over singular toric Calabi-Yau 4-folds. Triality translates into a local transformation of brane brick models, whose simplest representative is a cube move. We present explicit examples and construct their triality networks. We also argue that the classical mesonic moduli space of brane brick model theories, which corresponds to the probed Calabi-Yau 4-fold, is invariant under triality. Finally, we discuss triality in terms of phase boundaries, which play a central role in connecting Calabi-Yau 4-folds to brane brick models.