Abelian Orbifolds for Brane Brick Models
Abstract
We present a systematic procedure for constructing brane brick models corresponding to abelian orbifolds of toric Calabi-Yau 4-folds, extending the orbifold construction beyond the well-studied case of abelian orbifolds of C^4. Given a parent brane brick model corresponding to a toric Calabi-Yau 4-fold M, we show that the action of an abelian orbifold group Gamma on the generators of M induces an action on the chiral and Fermi fields as well as the J- and E-terms of the associated 2d (0,2) supersymmetric gauge theory. The requirement that the orbifolded brane brick model remains consistent with the closed paths associated with the J- and E-terms, together with the chiral cycles formed by their products, precisely reproduces the Calabi-Yau condition on the orbifold action. This procedure yields an explicit formula for the J- and E-terms of the orbifolded brane brick model in terms of those of the parent theory. We apply our construction to the brane brick models corresponding to Q^{1,1,1} and D_3, and present the resulting families of 2d (0,2) quiver gauge theories. We also present explicit expressions for generating functions that count distinct abelian orbifolds of Q^{1,1,1} and D_3.
Versions
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BibTeX
@misc{kwon2026abelian,
title = {{Abelian Orbifolds for Brane Brick Models}},
author = {Juno Kwon and Rak-Kyeong Seong},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.28110},
eprint = {2606.28110},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.28110},
}
RIS
TY - UNPB
TI - Abelian Orbifolds for Brane Brick Models
AU - Juno Kwon
AU - Rak-Kyeong Seong
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2606.28110
UR - https://arxiv.org/abs/2606.28110
AB - We present a systematic procedure for constructing brane brick models corresponding to abelian orbifolds of toric Calabi-Yau 4-folds, extending the orbifold construction beyond the well-studied case of abelian orbifolds of C^4. Given a parent brane brick model corresponding to a toric Calabi-Yau 4-fold M, we show that the action of an abelian orbifold group Gamma on the generators of M induces an action on the chiral and Fermi fields as well as the J- and E-terms of the associated 2d (0,2) supersymmetric gauge theory. The requirement that the orbifolded brane brick model remains consistent with the closed paths associated with the J- and E-terms, together with the chiral cycles formed by their products, precisely reproduces the Calabi-Yau condition on the orbifold action. This procedure yields an explicit formula for the J- and E-terms of the orbifolded brane brick model in terms of those of the parent theory. We apply our construction to the brane brick models corresponding to Q^{1,1,1} and D_3, and present the resulting families of 2d (0,2) quiver gauge theories. We also present explicit expressions for generating functions that count distinct abelian orbifolds of Q^{1,1,1} and D_3.
ER -