Chern-Simons corner phase spaces in BF-BB theories
- 1Perimeter Institute
Abstract
A bstract : We investigate an approach to determine corner Poisson brackets of fields restricted to codimension 2 and 3 surfaces in 4D theories, without making use of boundary conditions. Instead, within the example of BF-BB type theories, we show that the constraint/generator algebra on a partial Cauchy slice is enough to determine the Poisson brackets and a corner symplectic form, useful in extended phase space constructions or holography. The codimension 2 phase space turns out to be of Chern-Simons type, but lacking a flatness constraint. In a setting with codimension 3 surfaces, there is also a further Wess-Zumino-type current algebra. We apply this approach also to a specific formulation of full 4D gravity, based on the Maxwell algebra g=so(1,3)ltimes (ℝ1,3overset∼ ⊕so(1,3)∗) g = so 1 3 ⋉ ℝ 1 , 3 ⊕ ~ so 1 3 ∗ . This realises the corner Poisson bracket of the spin connection for the first time and shows it is off-shell commutative, while the corner metric is noncommutative.
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BibTeX
@article{langenscheidt2026chernsimons,
title = {{Chern-Simons corner phase spaces in BF-BB theories}},
author = {Simon Langenscheidt},
journal = {Journal of High Energy Physics},
year = {2026},
month = oct,
doi = {10.1007/jhep10(2026)028},
url = {https://link.springer.com/10.1007/JHEP10(2026)028},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Chern-Simons corner phase spaces in BF-BB theories
AU - Simon Langenscheidt
PY - 2026
DA - 2026/10/02
JO - Journal of High Energy Physics
DO - 10.1007/jhep10(2026)028
UR - https://link.springer.com/10.1007/JHEP10(2026)028
AB - A bstract : We investigate an approach to determine corner Poisson brackets of fields restricted to codimension 2 and 3 surfaces in 4D theories, without making use of boundary conditions. Instead, within the example of BF-BB type theories, we show that the constraint/generator algebra on a partial Cauchy slice is enough to determine the Poisson brackets and a corner symplectic form, useful in extended phase space constructions or holography. The codimension 2 phase space turns out to be of Chern-Simons type, but lacking a flatness constraint. In a setting with codimension 3 surfaces, there is also a further Wess-Zumino-type current algebra. We apply this approach also to a specific formulation of full 4D gravity, based on the Maxwell algebra g=so(1,3)ltimes (ℝ^1,3overset∼ ⊕so(1,3)^∗) g = so 1 3 ⋉ ℝ 1 , 3 ⊕ ~ so 1 3 ∗ . This realises the corner Poisson bracket of the spin connection for the first time and shows it is off-shell commutative, while the corner metric is noncommutative.
SN - 1029-8479
ER -