Symplectic Yang-Mills Theory
Abstract
On a symplectic manifold, any differential two-form has a natural decomposition into two components: a primitive part and a non-primitive one. Applying this decomposition to the curvature two-form of a principal bundle over a symplectic manifold, we obtain a natural splitting of the Yang-Mills (YM) functional into two functionals that intrinsically depend on the symplectic structure: the primitive Yang-Mills (PYM) functional and the trace Yang-Mills (TYM) functional. We work out the basic properties of the critical solutions of these two functionals. The PYM functional in particular exhibits many of the desirable properties of the YM functional, including the ellipticity of its Euler-Lagrange equations and an algebraic classification of its flat solutions on G-bundles. We also prove a monotonicity formula for the PYM functional as a first step towards characterizing its moduli space of solutions.
Related
- Eliminating the Higgs field and perturbing Yang-Mills connections in cone Yang-Mills theory
- Yang-Mills theory for multiplicative Ehresmann connections
- Towards General Relativity as a generalized Yang-Mills theory
- A Self-Dual Frame Formalism of the SO(3) Yang-Mills Theory
- Yang-Mills Theory in the Multisymplectic Framework
BibTeX
@misc{delgado2026symplectic,
title = {{Symplectic Yang-Mills Theory}},
author = {Jonathan Delgado and Li-Sheng Tseng and Jiawei Zhou},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.16112},
eprint = {2609.16112},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.16112},
}
RIS
TY - UNPB
TI - Symplectic Yang-Mills Theory
AU - Jonathan Delgado
AU - Li-Sheng Tseng
AU - Jiawei Zhou
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.16112
UR - https://arxiv.org/abs/2609.16112
AB - On a symplectic manifold, any differential two-form has a natural decomposition into two components: a primitive part and a non-primitive one. Applying this decomposition to the curvature two-form of a principal bundle over a symplectic manifold, we obtain a natural splitting of the Yang-Mills (YM) functional into two functionals that intrinsically depend on the symplectic structure: the primitive Yang-Mills (PYM) functional and the trace Yang-Mills (TYM) functional. We work out the basic properties of the critical solutions of these two functionals. The PYM functional in particular exhibits many of the desirable properties of the YM functional, including the ellipticity of its Euler-Lagrange equations and an algebraic classification of its flat solutions on G-bundles. We also prove a monotonicity formula for the PYM functional as a first step towards characterizing its moduli space of solutions.
ER -