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Higher Dressing and Shift-Invariance in 4D Topological BF Theory
Abstract
A characteristic feature of topological field theories is the absence of local propagating degrees of freedom. In four-dimensional BF theory with cosmological term, we make this feature manifest by exactly reducing the finite non-Abelian shift symmetry. We do so by identifying a higher dressing field, a 1-form compensating the shift, allowing to build from first principles the composite shift-invariant field B=B−λ−1F. In terms of this dressed field, the dynamics becomes algebraic and sets B=0, directly exposing the absence of local propagating degrees of freedom. This provides the first explicit instance of the higher-form Dressing Field Method.
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BibTeX
@misc{francois2026higher,
title = {{Higher Dressing and Shift-Invariance in 4D Topological BF Theory}},
author = {J. François and L. Ravera},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15737},
eprint = {2610.15737},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15737},
}
RIS
TY - UNPB
TI - Higher Dressing and Shift-Invariance in 4D Topological BF Theory
AU - J. François
AU - L. Ravera
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2610.15737
UR - https://arxiv.org/abs/2610.15737
AB - A characteristic feature of topological field theories is the absence of local propagating degrees of freedom. In four-dimensional BF theory with cosmological term, we make this feature manifest by exactly reducing the finite non-Abelian shift symmetry. We do so by identifying a higher dressing field, a 1-form compensating the shift, allowing to build from first principles the composite shift-invariant field B=B−λ^−1F. In terms of this dressed field, the dynamics becomes algebraic and sets B=0, directly exposing the absence of local propagating degrees of freedom. This provides the first explicit instance of the higher-form Dressing Field Method.
ER -