Current Reconstruction and Higher Interactions in Gauge Theory
Abstract
We revisit Deser's current reconstruction in first-order Yang--Mills theory with an independent two-form. We fix the quadratic auxiliary sector and the first gauge correction, and ask whether a prescribed curvature interaction can be added without higher-order action terms. For a compact semisimple gauge algebra, requiring the mixed Noether identity to close without a gh action term fixes the algebraic auxiliary representative to the tangent representative, up to linear curvature and dual-curvature terms on each simple ideal. For the analytic radial class U=Φ(f· f), with first nonlinear term cp(f· f)p, no allowed representative avoids a third-order action correction when all second-order action coefficients vanish. A free-field scaling argument inside a root su(2) subalgebra establishes this result for every compact semisimple gauge algebra. Ordinary covariantization and an auxiliary-field shift give an explicit completion. For p=2, its seven-gluon contact term cancels a nonzero tree-level Ward contraction at real nonsingular kinematics. We also study an affine star-gauge sector motivated by Seiberg--Witten maps, where strict current feedback and second-order action truncation select different representatives. Together these results show how the prescribed auxiliary data determine which interactions are required by current reconstruction.
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BibTeX
@misc{gregory2026current,
title = {{Current Reconstruction and Higher Interactions in Gauge Theory}},
author = {Carolina Matté Gregory},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19402},
eprint = {2609.19402},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19402},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Current Reconstruction and Higher Interactions in Gauge Theory
AU - Carolina Matté Gregory
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.19402
UR - https://arxiv.org/abs/2609.19402
AB - We revisit Deser's current reconstruction in first-order Yang--Mills theory with an independent two-form. We fix the quadratic auxiliary sector and the first gauge correction, and ask whether a prescribed curvature interaction can be added without higher-order action terms. For a compact semisimple gauge algebra, requiring the mixed Noether identity to close without a gh action term fixes the algebraic auxiliary representative to the tangent representative, up to linear curvature and dual-curvature terms on each simple ideal. For the analytic radial class U=Φ(f· f), with first nonlinear term c_p(f· f)^p, no allowed representative avoids a third-order action correction when all second-order action coefficients vanish. A free-field scaling argument inside a root su(2) subalgebra establishes this result for every compact semisimple gauge algebra. Ordinary covariantization and an auxiliary-field shift give an explicit completion. For p=2, its seven-gluon contact term cancels a nonzero tree-level Ward contraction at real nonsingular kinematics. We also study an affine star-gauge sector motivated by Seiberg--Witten maps, where strict current feedback and second-order action truncation select different representatives. Together these results show how the prescribed auxiliary data determine which interactions are required by current reconstruction.
ER -