2017/02/28 by Sebastian Franco, Dongwook Ghim, Sangmin Lee +1 · 1 citation
Physics and Astronomy · #hep-th
paper · pdf · doi:10.1007/jhep06(2017)068
published as JHEP 1706:068,2017 · 56 pages, 15 figures; v2. references added; v3. a reference and a comment on a fixed point index theorem added
arxiv created 2017/06/03 · arxiv updated 2017/07/14
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.