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

Abstract

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. In theories whose matter sector suffers from abelian gauge anomaly, we propose an ansatz for an anomaly cancelling term in the integral formula for the elliptic genus. We provide an example in which two brane brick models related to each other by Gadde-Gukov-Putrov triality give the same elliptic genus.

56 pages, 15 figures; v2. references added; v3. a reference and a comment on a fixed point index theorem added

References in corpus (8)

• Sasaki-Einstein Manifolds and Volume Minimisation
• Exact two-dimensional superconformal R-symmetry and c-extremization
• Brane Brick Models in the Mirror
• Brane Brick Models and 2d (0,2) Triality
• F-theory and 2d (0,2) Theories
• UV Completions for Non-Critical Strings
• Orbifold Reduction and 2d (0,2) Gauge Theories
• Localization of twisted $\mathcal{N}=(0,2)$ gauged linear sigma models in two dimensions

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