Regular-Zero Drinfeld-Sokolov Charges in Doubled Four-Dimensional Chern-Simons Theory
Abstract
We study classical local conserved charges obtained after finite-defect reduction of doubled four-dimensional Chern--Simons theory. At a finite simple zero, the inhomogeneous derivative term in the affine gauge transformation induced by the twist function vanishes, so the residue evaluations of the two Gaudin currents transform by the ordinary adjoint action. For each simple ideal, we use the Evans-compatible invariant tensors of the principal Drinfeld--Sokolov hierarchy as external algebraic input, construct local circle integrals, and treat the same-zero, distinct-zero, and mixed sectors separately, proving pairwise Poisson commutativity. Under the explicit assumptions of Stedman's simple-pole/simple-zero boundary Hamiltonian, the periodic trivial-monodromy sector, and boundary weights independent of phase-space variables, the reduced Hamiltonian decomposes term by term into finite-pole, infinity, finite-zero, and residual first-class-constraint contributions, which yields conservation of the constructed charges. We distinguish the finite-defect reduced space, the extended space carrying the residual constraint, and the physical quotient. The result is a conditional existence statement for a classical local Abelian Poisson subalgebra; we make no claim of functional independence, maximality, or Liouville completeness. Extensions to higher-order zeros and nontrivial monodromy sectors are outside the scope of this work.
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BibTeX
@misc{zeng2026regularzero,
title = {{Regular-Zero Drinfeld-Sokolov Charges in Doubled Four-Dimensional Chern-Simons Theory}},
author = {Wentao Zeng and Yifan He and Xian Wu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16271},
eprint = {2610.16271},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16271},
}
RIS
TY - UNPB
TI - Regular-Zero Drinfeld-Sokolov Charges in Doubled Four-Dimensional Chern-Simons Theory
AU - Wentao Zeng
AU - Yifan He
AU - Xian Wu
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16271
UR - https://arxiv.org/abs/2610.16271
AB - We study classical local conserved charges obtained after finite-defect reduction of doubled four-dimensional Chern--Simons theory. At a finite simple zero, the inhomogeneous derivative term in the affine gauge transformation induced by the twist function vanishes, so the residue evaluations of the two Gaudin currents transform by the ordinary adjoint action. For each simple ideal, we use the Evans-compatible invariant tensors of the principal Drinfeld--Sokolov hierarchy as external algebraic input, construct local circle integrals, and treat the same-zero, distinct-zero, and mixed sectors separately, proving pairwise Poisson commutativity. Under the explicit assumptions of Stedman's simple-pole/simple-zero boundary Hamiltonian, the periodic trivial-monodromy sector, and boundary weights independent of phase-space variables, the reduced Hamiltonian decomposes term by term into finite-pole, infinity, finite-zero, and residual first-class-constraint contributions, which yields conservation of the constructed charges. We distinguish the finite-defect reduced space, the extended space carrying the residual constraint, and the physical quotient. The result is a conditional existence statement for a classical local Abelian Poisson subalgebra; we make no claim of functional independence, maximality, or Liouville completeness. Extensions to higher-order zeros and nontrivial monodromy sectors are outside the scope of this work.
ER -