Perturbative Holonomy Potentials and Vacua in Chiral Supersymmetric Gauge Theories
Abstract
We establish global control of perturbative D-term data governing semiclassical vacuum sectors in chiral supersymmetric gauge theories on ℝ3× S1. A closed-form, one-loop-exact D-term coefficient, including 4d Fayet--Iliopoulos (FI) parameters, gives a uniformly controlled leading potential away from massless thresholds and fixes local FI and Chern--Simons couplings near them. This allows lifting the 3d Intriligator--Seiberg classification of semiclassical vacua to ℝ3× S1 across the compact holonomy space. The framework is showcased by finding a remarkably rich set of vacuum sectors in a simple abelian model and reproducing on flat space the R-twisted reduction of an SU(2) Maruyoshi--Song theory to the Gang--Yamazaki theory, first found on S3× S1. The examples demonstrate the stakes of global matching: true vacua may lie at nontrivial holonomy even with nonzero threshold values of the Coulomb-slice D-coefficient, and despite vanishing D-coefficient at trivial holonomy.
Related
- Vacuum Structure of Maximally Supersymmetric Two-Dimensional Gauge Theories
- Quantum Elliptic Cohomology From Four-Dimensional Minimal Supersymmetric Gauge Theories
- Towards Wedge Construction of Four-Dimensional Non-Supersymmetric Theories and Torsion Classes
- Higher Groupoids of Gauge Potentials in Higher Gauge Theories admitting Weights
- Integrable Chiral Quantum Field Theories with Spacetime-Dependent Interactions
BibTeX
@misc{ardehali2026perturbative,
title = {{Perturbative Holonomy Potentials and Vacua in Chiral Supersymmetric Gauge Theories}},
author = {Arash Arabi Ardehali},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.34240},
eprint = {2610.34240},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.34240},
}
RIS
TY - UNPB
TI - Perturbative Holonomy Potentials and Vacua in Chiral Supersymmetric Gauge Theories
AU - Arash Arabi Ardehali
PY - 2026
DA - 2026/10/25
PB - arXiv
DO - 10.48550/arxiv.2610.34240
UR - https://arxiv.org/abs/2610.34240
AB - We establish global control of perturbative D-term data governing semiclassical vacuum sectors in chiral supersymmetric gauge theories on ℝ^3× S^1. A closed-form, one-loop-exact D-term coefficient, including 4d Fayet--Iliopoulos (FI) parameters, gives a uniformly controlled leading potential away from massless thresholds and fixes local FI and Chern--Simons couplings near them. This allows lifting the 3d Intriligator--Seiberg classification of semiclassical vacua to ℝ^3× S^1 across the compact holonomy space. The framework is showcased by finding a remarkably rich set of vacuum sectors in a simple abelian model and reproducing on flat space the R-twisted reduction of an SU(2) Maruyoshi--Song theory to the Gang--Yamazaki theory, first found on S^3× S^1. The examples demonstrate the stakes of global matching: true vacua may lie at nontrivial holonomy even with nonzero threshold values of the Coulomb-slice D-coefficient, and despite vanishing D-coefficient at trivial holonomy.
ER -