Flat Gauging of Continuous (Non-invertible) Symmetries and Non-compact BF SymTFT for Compact Boson
Abstract
We study flat gauging of continuous symmetries by summing over flat gauge-field configurations. We focus on the two-dimensional compact boson and construct the torus partition function with general flat U(1)M× U(1)W backgrounds. We show that flat gauging either U(1)M or U(1)W decompactifies the theory to the non-compact free boson, and that the dual ℤ background combines with the remaining U(1) background into a non-compact ℝ symmetry background due to the mixed anomaly. We also revisit the self-dual radius, where flat gauging the diagonal SO(3)⊂ (SU(2)L× SU(2)R)/ℤ2, first pointed out by Gaberdiel and Suchanek, gives the continuous orbifold which lies outside the usual c=1 moduli space. On the orbifold branch, we study finite and continuous non-invertible flat gaugings and explain why the continuous case requires a prescription for zero-measure fixed loci on the moduli space. Finally, we formulate the SymTFT of torus sigma models as a non-compact BF theory, whose topological boundary states encode the Narain moduli space and the O(D,D;ℤ) T-duality action.
Related
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- All Symmetries and Boundaries of the Two-Dimensional Free Scalar from Continuous Flat-Gauging
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- Symmetry defects and gauging for quantum states with matrix product unitary symmetries
BibTeX
@misc{jia2026flat,
title = {{Flat Gauging of Continuous (Non-invertible) Symmetries and Non-compact BF SymTFT for Compact Boson}},
author = {Qiang Jia and Yi Zhang},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2606.15732},
eprint = {2606.15732},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.15732},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Flat Gauging of Continuous (Non-invertible) Symmetries and Non-compact BF SymTFT for Compact Boson
AU - Qiang Jia
AU - Yi Zhang
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2606.15732
UR - https://arxiv.org/abs/2606.15732
AB - We study flat gauging of continuous symmetries by summing over flat gauge-field configurations. We focus on the two-dimensional compact boson and construct the torus partition function with general flat U(1)_M× U(1)_W backgrounds. We show that flat gauging either U(1)_M or U(1)_W decompactifies the theory to the non-compact free boson, and that the dual ℤ background combines with the remaining U(1) background into a non-compact ℝ symmetry background due to the mixed anomaly. We also revisit the self-dual radius, where flat gauging the diagonal SO(3)⊂ (SU(2)_L× SU(2)_R)/ℤ_2, first pointed out by Gaberdiel and Suchanek, gives the continuous orbifold which lies outside the usual c=1 moduli space. On the orbifold branch, we study finite and continuous non-invertible flat gaugings and explain why the continuous case requires a prescription for zero-measure fixed loci on the moduli space. Finally, we formulate the SymTFT of torus sigma models as a non-compact BF theory, whose topological boundary states encode the Narain moduli space and the O(D,D;ℤ) T-duality action.
ER -