Abstract
Brane brick models are Type IIA brane configurations that encode the 2d mathcal{N}=left(0,2right) gauge theories on the worldvolume of D1-branes probing toric Calabi-Yau 4-folds. We use mirror symmetry to improve our understanding of this correspondence and to provide a systematic approach for constructing brane brick models starting from geometry. The mirror configuration consists of D5-branes wrapping 4-spheres and the gauge theory is determined by how they intersect. We also explain how 2d (0, 2) triality is realized in terms of geometric transitions in the mirror geometry. Mirror symmetry leads to a geometric unification of dualities in different dimensions, where the order of duality is n − 1 for a Calabi-Yau n-fold. This makes us conjecture the existence of a quadrality symmetry in 0d. Finally, we comment on how the M-theory lift of brane brick models connects to the classification of 2d (0, 2) theories in terms of 4-manifolds.
Highlights
The interplay between Calabi-Yau (CY) geometry and branes probing it has played a key role in understanding duality symmetries of field theories that emerge in string theory. D-branes probing CY singularities have given rise to an interesting class of SCFT’s
We use mirror symmetry to improve our understanding of this correspondence and to provide a systematic approach for constructing brane brick models starting from geometry
The mirror configuration consists of D5-branes wrapping 4-spheres and the gauge theory is determined by how they intersect
Summary
The interplay between Calabi-Yau (CY) geometry and branes probing it has played a key role in understanding duality symmetries of field theories that emerge in string theory. D1-branes probing CY 4-fold singularities were considered in [9,10,11], where the corresponding gauge theories they give rise to were proposed. These theories lead to 2d (0, 2) SCFT’s. This paper is mainly devoted to the 2d (0, 2) gauge theories that arise on the worldvolume of D1-branes probing singular toric CY 4-folds. We focus on theories in which all fields transform in either bifundamental or adjoint representations of a i U(Ni) gauge group and can be represented by quiver diagrams as shown in figure 1
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