AI 中文总结
该论文用光前方法分析四次阶庞加莱代数封闭性，求解光锥约束，分类高自旋理论，阐明相关代数与约束的关系，证实杨-米尔斯理论等存在性，确定高自旋四点振幅。
AI 中文摘要
本论文采用光前方法研究四维无质量高自旋相互作用，通过分析四次阶庞加莱代数的封闭性展开研究。首先，在平直空间中求解光锥四次全纯约束，证明存在无穷多相互作用的局域高自旋理论，其场数量有限或无穷，并对所有含1阶和2阶导数的理论进行分类，对应规范与引力相互作用的高自旋推广，这些是自对偶杨-米尔斯理论和引力的高自旋推广的自洽子 sector，本身为手征高自旋引力的截断。接着，阐明共形场论（celestial CFT）中的算子乘积展开（OPE）结合性、一般运动学下树级振幅为零、相关“规范代数”（运动学代数）的雅可比恒等式与光锥全纯约束之间的关系。最后，研究涉及最大螺旋度违反（MHV）和反最大螺旋度违反（anti-MHV）顶点的非全纯四次约束，证实杨-米尔斯理论和引力的存在，以及多引力子相互作用理论的不自洽性；还表明纳入高阶导数三次顶点后，存在满足全四次约束的非平凡解，分类所有幺正局域高自旋理论，识别新的局域准手征理论族，并利用旋量螺旋度形式及自洽因式分解形式的局域性确定所有局域高自旋四点振幅。
英文摘要
This thesis studies $4d$ massless higher-spin interactions in the Light-Front approach by analysing the closure of the Poincaré algebra at quartic order. We first solve the light-cone quartic holomorphic constraint in flat space and show the existence of infinitely many interacting local higher-spin theories with either a finite or infinite number of fields. We classify all one- and two-derivative theories, corresponding to higher-spin extensions of gauge and gravitational interactions. These are consistent subsectors of higher-spin extensions of self-dual Yang--Mills and gravity, themselves truncations of Chiral Higher-Spin Gravity. We then clarify the relation between the OPE associativity in celestial CFT, the vanishing of tree-level amplitudes for generic kinematics, the Jacobi identity of the associated ''gauge algebra'' (kinematical algebra), and the light-cone holomorphic constraints. Finally, we investigate the non-holomorphic quartic constraint involving both MHV and anti-MHV vertices. We recover the existence of Yang-Mills theory and gravity, and the inconsistency of interacting multi-graviton theories. We then show that once higher-derivative cubic vertices are included, nontrivial solutions to the full quartic constraint exist. We classify all unitary local higher-spin theories, identify new families of local quasi-chiral theories, and determine all local higher-spin four-point amplitudes using the spinor-helicity formalism together with locality in the form of consistent factorisation.
CommentsPhD thesis, UMONS 2025; based on [arXiv:2505.12839], [arXiv:2508.16804], [arXiv:2602.12826]
