天体引力中的度规源完备化与可积性
Metric Source Completions and Integrability in Celestial Gravity
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中文总结 AI 辅助
本文通过Weyl-Beltrami变量评估天体爱因斯坦散射的局域度规源响应，提出完备化条件并验证可积性，为天体度规源完备化提供物理响应数据与延拓域。
中文摘要 AI 辅助
我们在Weyl-Beltrami变量中评估了天体爱因斯坦散射的局域度规源响应。紧致物理引力子波包保留了动量守恒分布及其法向导数。对于不相交的光滑Beltrami轮廓，完整的参考同手性Ward响应在二次阶上与微分的拟共形源泛函一致。减去对称化乘积响应后，得到一个非零的非线性坐标贡献，该贡献可由线性法向波包独立于二次法向系数检测到。解析法向轮廓子类支持在紧致未收缩区域上的角向延拓，并允许评估MHV能量角点和相对的Banerjee-Pasterski端点留数。对于相反螺旋度，连续的软定理确定了完整动量分布中的能量和自旋贡献。一个实Kawai-Lewellen-Tye通道给出了其非零法向系数和引力接触项的混合Mellin因子。我们为混合度规Hessian制定了额外的全局Ward、接触和延拓条件。参考散射数据、源输运和真空完备化在此构造中分别进入。在标量扇区中，面积归一化的相对行列式确定了反常泛函，固定面积调和组合从有界导数阶的局域曲率项中提取其Euler系数。这些计算为可积天体度规源完备化提供了物理响应数据和局域延拓域。
英文摘要
We study metric-source responses of celestial Einstein amplitudes while retaining their momentum-conservation distribution. The consecutive opposite-helicity response is related to the simultaneous gravitational contact at arbitrary hard multiplicity. Their difference contains a Lorentz transformation that annihilates the conservation delta function, determining the normal recoil contribution and its relation to the undifferentiated coefficient. A six-graviton tree calculation evaluates both coefficients on a real scattering channel. For the summed homogeneous contact, momentum conservation cancels the leading angular singularities. Uniform bounds at coincident soft directions and hard punctures yield integrated endpoint estimates that determine the ordered Mellin residues after smooth source smearing. The mixed Mellin divisor also retains logarithms of soft--hard invariant ratios at generic conformal weight. In Weyl--Beltrami variables, the quadratic reference Ward response combines soft-leg, shadow-map and spin-frame terms into the transported metric Hessian, with a nonzero symmetric mixed susceptibility. Relative shadow primitives require boundary currents when represented across logarithmic cuts; their source variation fixes the accompanying contour contribution. Joint factorization and angular expansions organize the additional NMHV relative-contour terms into residue coefficients that distinguish metric integrability from matching to a specified source functional. An independent vacuum completion supplies the Euler response, which fixed-area harmonic combinations separate from local curvature terms at bounded derivative order.
发表机构
- Zhongtai Securities Institute for Financial Studies, Shandong University（山东大学中泰金融研究院）
- Department of Physics, Southern Methodist University（南方卫理公会大学物理系）
- School of Statistics, Dongbei University of Finance and Economics（东北财经大学统计学院）
机构由 AI 辅助整理，请以论文原文为准。
