AI 中文总结
本文综述四维量子引力理论SDG与SDYM，推导其自对偶作用量等关键内容，填补文献空白，指出研究方向，还提及天体全息论相关结果。
AI 中文摘要
自对偶爱因斯坦引力（SDG）是四维中一种单圈精确、紫外和红外有限、微分同胚不变的非酉量子引力理论，其唯一非平凡振幅为单圈全正号振幅，且与纯爱因斯坦引力的对应振幅相等。本文以教学方式综述SDG与自对偶杨-米尔斯理论（SDYM），引导读者完成关键计算，填补文献中的部分空白，并指出未来研究方向。涵盖主题包括：从光锥规范下的完整爱因斯坦引力/杨-米尔斯作用量推导自对偶作用量、鬼场退耦、Berends-Giele流、树级单负号振幅的消失、天体Lw₁₊∞对称性、微扰子、SDYM与SDG单圈全正号振幅的双离壳流计算、维度偏移、幺正切割、BDPR引力公式、单圈色序，以及自对偶理论的协变形式及其规范固定。还综述了天体全息论项目的部分精选结果，并简要提及单圈单负号引力振幅的全n表达式。
英文摘要
Self-dual Einstein gravity is a one-loop exact, UV and IR finite, diffeomorphism invariant, non-unitary theory of quantum gravity in four dimensions. The only non-trivial amplitudes are the one-loop-all-plus amplitudes, and they are equal to those of pure Einstein gravity. In these notes we review SDG and SDYM pedagogically. We walk the reader through key calculations, fill in some gaps in the literature, and point out directions for future research. Topics include: derivation of the self-dual actions from the full Einstein gravity/YM actions in lightcone gauge, decoupling of ghosts, Berends-Giele currents, vanishing of tree-level-one-minus amplitudes, celestial $Lw_{1+\infty}$ symmetry, perturbiners, double-off-shell current calculation of one-loop-all-plus SDYM and SDG amplitudes, dimension shifting, unitarity cuts, the BDPR gravity formula, one-loop color ordering, and the covariant formulations of the self-dual theories as well as their their gauge fixing. We also review some selected results from the celestial holography program, and briefly comment on an all-n expression for the one-loop-one-minus gravity amplitudes.
Comments77 pages + 8 appendices
