规范理论中的流重构与高阶相互作用
Current Reconstruction and Higher Interactions in Gauge Theory
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中文总结 AI 辅助
本文在二阶杨-米尔斯理论中研究Deser流重构，证明对紧致半单规范代数，指定曲率相互作用通常需三阶作用修正，并给出显式完备化及七胶子接触项抵消Ward收缩的实例。
中文摘要 AI 辅助
我们重新审视具有独立二形式的二阶杨-米尔斯理论中的Deser流重构。我们固定二次辅助扇区和首次规范修正，并询问在无高阶作用项的情况下，是否可以添加指定的曲率相互作用。对于紧致半单规范代数，要求混合Noether恒等式在无$gh$作用项的情况下闭合，将代数辅助代表固定为切代表，直至每个单理想上的线性曲率和双曲率项。对于解析径向类$U=\Phi(f\cdot f)$，其首个非线性项为$c_p(f\cdot f)^p$，当所有二阶作用系数为零时，没有任何允许的代表能避免三阶作用修正。根$\mathfrak{su}(2)$子代数内的自由场标度论证为每个紧致半单规范代数确立了这一结果。普通协变化和辅助场位移给出了显式完备化。对于$p=2$，其七胶子接触项在实非奇异运动学下抵消了非零树级Ward收缩。我们还研究了受Seiberg-Witten映射启发的仿射星规范扇区，其中严格的流反馈和二阶作用截断选择了不同的代表。这些结果共同表明，规定的辅助数据如何决定流重构所需的相互作用。
英文摘要
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 $U=Φ(f\cdot f)$, with first nonlinear term $c_p(f\cdot f)^p$, no allowed representative avoids a third-order action correction when all second-order action coefficients vanish. A free-field scaling argument inside a root $\mathfrak{su}(2)$ 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.
发表机构
- Universidade de Brasília, Instituto de Física（巴西利亚大学物理研究所）
- International Center of Physics（国际物理中心）
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