In this work, we study the symmetry breaking conditions, given by a (anti)de Sitter-valued vector field, of a full (anti)de Sitter-invariant MacDowell–Mansouri inspired action. We show that under these conditions, the action breaks down to General Relativity with a cosmological constant, the four-dimensional topological invariants, as well as the Holst term. We obtain the equations of motion of this action, and analyze the symmetry breaking conditions.

中文翻译：

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MacDowell-Mansouri 作用中对称破缺条件的评论

在这项工作中，我们研究了由（反）de Sitter 值向量场给出的完全（反）de Sitter 不变的 MacDowell-Mansouri 启发作用的对称破缺条件。我们表明，在这些条件下，作用分解为具有宇宙常数、四维拓扑不变量以及 Holst 项的广义相对论。我们得到了这个动作的运动方程，并分析了对称破缺条件。