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arXiv · 2610.15737

Higher Dressing and Shift-Invariance in 4D Topological BF Theory

J. François·L. Ravera
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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 $\boldsymbol{B}=B-λ^{-1}F$. In terms of this dressed field, the dynamics becomes algebraic and sets $\boldsymbol{B}=0$, 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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J. François, L. Ravera. 2026-10-11. Higher Dressing and Shift-Invariance in 4D Topological BF Theory. https://arxiv.org/abs/2610.15737

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