Toral Chern-Simons TQFT via Geometric Quantization in Real Polarization
Mathematical Physics
2026-04-02 v1 Strongly Correlated Electrons
High Energy Physics - Theory
math.MP
Quantum Algebra
Abstract
We construct toral Chern-Simons theory with gauge group from an even, integral, nondegenerate symmetric bilinear form by geometric quantization via real polarization. We obtain a unitary extended -dimensional TQFT by constructing the boundary state spaces and canonical operators and proving that they satisfy the cylinder and gluing axioms. The finite discriminant group arises naturally in the theory and controls the genus- state spaces. At genus one, the theory recovers the finite quadratic data underlying bosonic Abelian topological order.
Keywords
Cite
@article{arxiv.2604.01016,
title = {Toral Chern-Simons TQFT via Geometric Quantization in Real Polarization},
author = {Daniel Galviz},
journal= {arXiv preprint arXiv:2604.01016},
year = {2026}
}