We present the deep connections among (Anti) de Sitter geometry, and complex conformal gravity-Maxwell theory, stemming directly from a gauge theory of gravity based on the complex Clifford algebra Cl(4, C). This is attained by simply promoting the de (Anti) Sitter algebras so(4, 1), so(3, 2) to the real Clifford algebras Cl(4, 1, R), Cl(3, 2, R), respectively. This interplay between gauge theories of gravity based on Cl(4, 1, R), Cl(3, 2, R) , whose bivector-generators encode the de (Anti) Sitter algebras so(4, 1), so(3, 2), respectively, and 4D conformal gravity based on Cl(3, 1, R) is reminiscent of the \(AdS_{ D+1}/CFT_D\) correspondence between \(D+1\)-dim gravity in the bulk and conformal field theory in the D-dim boundary. Although a plausible cancellation mechanism of the cosmological constant terms appearing in the real-valued curvature components associated with complex conformal gravity is possible, it does not occur simultaneously in the imaginary curvature components. Nevertheless, by including a Lagrange multiplier term in the action, it is still plausible that one might be able to find a restricted set of on-shell field configurations leading to a cancellation of the cosmological constant in curvature-squared actions due to the coupling among the real and imaginary components of the vierbein. We finalize with a brief discussion related to \(U(4) \times U(4)\) grand-unification models with gravity based on \( Cl (5, C) = Cl(4,C) \oplus Cl(4,C)\). It is plausible that these grand-unification models could also be traded for models based on \( GL (4, C) \times GL(4, C) \).

我们提出了（反）德西特几何和复杂的共形引力-麦克斯韦理论之间的深层联系，这些联系直接源于基于复杂的克利福德代数Cl (4,  C ) 的引力规范理论。这是通过简单地将德（反）西特代数so (4, 1)、  so (3, 2) 分别提升为实 Clifford 代数Cl (4, 1,  R )、  Cl (3, 2,  R )来实现的。基于Cl (4, 1,  R )、  Cl (3, 2,  R) ，其双向量生成器分别编码 de (反) Sitter 代数so (4, 1)、  so (3, 2)，并且基于Cl (3, 1,  R ) 的 4 D共形引力让人想起\ (AdS_{ D+1}/CFT_D\)体积中的\(D+1\) -dim 重力与D -dim 边界中的共形场论之间的对应关系。尽管与复共形引力相关的实值曲率分量中出现的宇宙常数项的合理抵消机制是可能的，但它并不可行。虚曲率分量同时发生。尽管如此，通过在作用中包含拉格朗日乘子项，人们仍然有可能找到一组有限的壳上场配置，从而由​​于之间的耦合而导致曲率平方作用中的宇宙学常数被抵消。 vierbein 的实部和虚部。我们最后简要讨论了与\(U(4) \times U(4)\)引力大统一模型相关的基于\( Cl (5, C) = Cl(4,C) \oplus Cl(4 ,C)\)。似乎这些大统一模型也可以交换为基于\( GL (4, C) \times GL(4, C) \) 的模型。