Generalized Symmetries of QED4 on Non-Spin Manifolds
Abstract
Generalized symmetries are sensitive to the tangential structure of spacetime. We study this interplay for massless QED on oriented non-spin four-manifolds, where the photon becomes a spinc connection and the path integral sums over spinc structures. The shifted flux quantization extends the magnetic 1-form symmetry into a w2-twisted 1-form symmetry: its 2π rotation acts as a gravitational sign, fixed by the normal bundle of the surface the operator wraps. The obstruction to treating it as an ordinary magnetic 1-form symmetry is an order-two mixed magnetic-gravitational anomaly, which is classified by reduced oriented bordism and detected on the Wu manifold. In a fixed spinc sector, this anomaly is removable by a counterterm, so it is a property of the sum over spinc structures. We discuss its consequences for gapped, Coulomb, and Higgs phases. The chiral anomaly is governed by the index of the spinc Dirac operator, so rational chiral defects carry gravitational as well as electromagnetic responses. A spinc Hall topological field theory cancels the electromagnetic part but leaves a framing anomaly. At the level of anomaly inflow, this is canceled for every rational angle by stacking a neutral, generally noninvertible Witten-Reshetikhin-Turaev layer. The same framing subtlety affects the chiral defects of QED on curved spin manifolds. The complex projective plane illustrates each of these features explicitly.
Related
- Nonlocal Equations on Domains and Manifolds Without Symmetries
- Scaling Symmetries and Conformal Relative Equilibria on Poisson Manifolds, with Applications to Lie-Poisson Systems
- Higher Integrability, Generalized Symmetries, and Partially Topological Field Theories
- Cartan-Ambrose-Hicks theorems and dual geodesic symmetries on statistical manifolds
- Scaling Symmetries and Conformal Relative Equilibria on Poisson Manifolds, with Applications to Lie-Poisson Systems
BibTeX
@misc{zotto2026generalized,
title = {{Generalized Symmetries of QED$_4$ on Non-Spin Manifolds}},
author = {Michele Del Zotto and Vivek Saxena},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38907},
eprint = {2610.38907},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38907},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Generalized Symmetries of QED_4 on Non-Spin Manifolds
AU - Michele Del Zotto
AU - Vivek Saxena
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38907
UR - https://arxiv.org/abs/2610.38907
AB - Generalized symmetries are sensitive to the tangential structure of spacetime. We study this interplay for massless QED on oriented non-spin four-manifolds, where the photon becomes a spin^c connection and the path integral sums over spin^c structures. The shifted flux quantization extends the magnetic 1-form symmetry into a w_2-twisted 1-form symmetry: its 2π rotation acts as a gravitational sign, fixed by the normal bundle of the surface the operator wraps. The obstruction to treating it as an ordinary magnetic 1-form symmetry is an order-two mixed magnetic-gravitational anomaly, which is classified by reduced oriented bordism and detected on the Wu manifold. In a fixed spin^c sector, this anomaly is removable by a counterterm, so it is a property of the sum over spin^c structures. We discuss its consequences for gapped, Coulomb, and Higgs phases. The chiral anomaly is governed by the index of the spin^c Dirac operator, so rational chiral defects carry gravitational as well as electromagnetic responses. A spin^c Hall topological field theory cancels the electromagnetic part but leaves a framing anomaly. At the level of anomaly inflow, this is canceled for every rational angle by stacking a neutral, generally noninvertible Witten-Reshetikhin-Turaev layer. The same framing subtlety affects the chiral defects of QED on curved spin manifolds. The complex projective plane illustrates each of these features explicitly.
ER -