Brane Brick Models for the Sasaki-Einstein 7-Manifolds Y^{p,k}(CP^1 x CP^1) and Y^{p,k}(CP^2)

TL;DR

This paper classifies 2d (0,2) supersymmetric gauge theories associated with specific Sasaki-Einstein 7-manifolds, providing the largest known set of such theories linked to Calabi-Yau 4-folds with explicit metrics.

Contribution

It introduces brane brick models for Y^{p,k}(CP^1 x CP^1) and Y^{p,k}(CP^2), expanding the classification of gauge theories for these geometries.

Findings

Identified gauge theories for Y^{p,k}(CP^1 x CP^1) and Y^{p,k}(CP^2)

Provided explicit metrics and toric diagrams for these manifolds

Established the largest classification of related 2d (0,2) theories

Abstract

The 2d (0,2) supersymmetric gauge theories corresponding to the classes of Y^{p,k}(CP^1 x CP^1) and Y^{p,k}(CP^2) manifolds are identified. The complex cones over these Sasaki-Einstein 7-manifolds are non-compact toric Calabi-Yau 4-folds. These infinite families of geometries are the largest ones for Sasaki-Einstein 7-manifolds whose metrics, toric diagrams, and volume functions are known explicitly. This work therefore presents the largest classification of 2d (0,2) supersymmetric gauge theories corresponding to Calabi-Yau 4-folds with known metrics.