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

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.

66 pages, 50 figures. v2: references and minor clarification added

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• Exact two-dimensional superconformal R-symmetry and c-extremization
• Two-dimensional SCFTs from D3-branes
• 2d (0,2) Quiver Gauge Theories and D-Branes
• Quivers, YBE and 3-manifolds
• Brane Brick Models, Toric Calabi-Yau 4-Folds and 2d (0,2) Quivers
• Exact quantization conditions for cluster integrable systems
• Integrability from 2d N=(2,2) Dualities
• Chiral operators in two-dimensional (0,2) theories and a test of triality
• Geometric Constructions of Two Dimensional (0,2) SUSY Theories
• Holomorphy, triality and non-perturbative beta function in 2d supersymmetric QCD

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