AI 中文总结
该研究在三类理论的受限扇区间构建非微扰经典双重拷贝对应，用多种剖面说明可映射解字典，为Kerr-Schild双重拷贝提供新实例。
AI 中文摘要
我们在四次双伴随标量理论、复SU(2)杨-米尔斯理论，以及具有共形平坦度量和无迹能量动量的四维广义相对论的受限假设扇区之间，构建了一种精确的解生成对应关系。因子化双伴随场、Corrigan–Fairlie–'t Hooft–Wilczek规范势和共形度量由共同的标量种子生成，它们的运动方程在耦合识别下简化为相同的运动方程，该对应关系的三个分支均保留非线性动力学。标量方程仅捕获爱因斯坦方程的迹，推导爱因斯坦方程的无迹部分还会得到引力与杨-米尔斯之间的源关系。由此，我们在四次双伴随标量理论、SU(2)杨-米尔斯理论和引力之间的受限假设扇区中构建了非微扰经典双重拷贝。我们用代表AdS₄、平面dS₄和闵可夫斯基空间的有理与常数剖面，以及雅可比椭圆剖面（针对负宇宙学常数生成正能量再坍缩分支，针对正宇宙学常数生成负能量反弹分支）来说明可映射解的对应字典，基于此我们提供了Kerr-Schild双重拷贝的新实例。
英文摘要
We construct an exact solution-generating correspondence between restricted ansatz sectors of quartic biadjoint scalar theory, complexified $SU(2)$ Yang--Mills theory and four-dimensional general relativity with conformally flat metrics and traceless energy-momentum. A factorised biadjoint field, a Corrigan--Fairlie--'t Hooft--Wilczek gauge potential and a conformal metric are generated by a common scalar seed. Their equations of motion reduce to the same equation of motion under the identification of couplings, which retains the nonlinear dynamics on all three legs of the correspondence. The scalar equation captures only the trace of the Einstein equations; deriving the trace-free part of the Einstein equation additionally yields a source relation between Gravity and Yang-Mills. From this, we construct a non-perturbative classical double copy for the restricted ansatz sectors between quartic biadjoint scalar theory, $SU(2)$ Yang--Mills theory and gravity. We illustrate the dictionary of mappable solutions with rational and constant profiles representing $AdS_4$, planar $dS_4$ and Minkowski space, and with Jacobi-elliptic profiles generating a positive-energy recollapsing branch for negative cosmological constant and a negative-energy bouncing branch for positive cosmological constant. Using these results, we provide a new example of the Kerr-Schild double copy.
