Supergroup Gauged Linear Sigma Models and their Physical Mathematics
Abstract
We construct 2d 𝒩=(2,2) gauged linear sigma models with U(1|1)N supergauge group possibly with superpotential. Despite being nonunitary, one can still study their space of supersymmetric states and explore their applications to mathematics. In particular, we find a relation between a nonlinear sigma model on a Calabi-Yau complete intersection of hypersurfaces in a super-Grassmannian and a supergauged Landau-Ginzburg orbifold, which can reduce to a regular Calabi-Yau/Landau-Ginzburg correspondence for complete intersections. This defines a super-Grassmannian/supergroup generalization of the correspondence proved by Clader [1] and Zhao [2]. Similarly, we find a relation between a nonlinear sigma model on a Calabi-Yau hypersurface in a product of super-Grassmannians and a hybrid NLSM/supergauged Landau-Ginzburg orbifold, which can reduce to a regular hybrid Calabi-Yau/Landau-Ginzburg correspondence for hypersurfaces in product space. This defines a super-Grassmannian/supergroup generalization of the correspondence proved by Fan-Jarvis-Ruan [3]. We also find that Calabi-Yau supervector bundles over a super-Grassmannian can undergo a physically related mild topology change which is reducible to a regular Atiyah-type flop transition. This defines a super-Grassmannian generalization of a birational equivalence of Calabi-Yau vector bundles in mathematics. Similarly, we find that a Calabi-Yau complete intersection of quadrics in a super-Grassmannian can also undergo a physically related topology change which is reducible to a regular conifold transition. This defines a super-Grassmannian generalization of a homological projective duality for Calabi-Yau quadrics by Kuznetsov-Perry [4] in mathematics.
Related
BibTeX
@misc{er2026supergroup,
title = {{Supergroup Gauged Linear Sigma Models and their Physical Mathematics}},
author = {Arif Er and Zhangcheng Liu and Meng-Chwan Tan},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.19775},
eprint = {2608.19775},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.19775},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Supergroup Gauged Linear Sigma Models and their Physical Mathematics
AU - Arif Er
AU - Zhangcheng Liu
AU - Meng-Chwan Tan
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2608.19775
UR - https://arxiv.org/abs/2608.19775
AB - We construct 2d 𝒩=(2,2) gauged linear sigma models with U(1|1)^N supergauge group possibly with superpotential. Despite being nonunitary, one can still study their space of supersymmetric states and explore their applications to mathematics. In particular, we find a relation between a nonlinear sigma model on a Calabi-Yau complete intersection of hypersurfaces in a super-Grassmannian and a supergauged Landau-Ginzburg orbifold, which can reduce to a regular Calabi-Yau/Landau-Ginzburg correspondence for complete intersections. This defines a super-Grassmannian/supergroup generalization of the correspondence proved by Clader [1] and Zhao [2]. Similarly, we find a relation between a nonlinear sigma model on a Calabi-Yau hypersurface in a product of super-Grassmannians and a hybrid NLSM/supergauged Landau-Ginzburg orbifold, which can reduce to a regular hybrid Calabi-Yau/Landau-Ginzburg correspondence for hypersurfaces in product space. This defines a super-Grassmannian/supergroup generalization of the correspondence proved by Fan-Jarvis-Ruan [3]. We also find that Calabi-Yau supervector bundles over a super-Grassmannian can undergo a physically related mild topology change which is reducible to a regular Atiyah-type flop transition. This defines a super-Grassmannian generalization of a birational equivalence of Calabi-Yau vector bundles in mathematics. Similarly, we find that a Calabi-Yau complete intersection of quadrics in a super-Grassmannian can also undergo a physically related topology change which is reducible to a regular conifold transition. This defines a super-Grassmannian generalization of a homological projective duality for Calabi-Yau quadrics by Kuznetsov-Perry [4] in mathematics.
ER -