We present new action principles for unimodular gravity, defined in the chiral Plebański formulation based on (complex) two-forms and a complex SO(3) connection. In these theories, just as in their analogues in the metric formulation, the cosmological constant does not take a prescribed value but is an integration constant whose value can differ between different (classical) solutions. We discuss some subtleties when identifying Lorentzian solutions in the generally complex theory, and show how these theories can be reduced to a ‘pure connection’ form similar to Krasnov’s pure connection formalism for general relativity.

中文翻译：

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幺模普列班斯基引力

我们提出了单模引力的新作用原理，该原理在基于（复）两种形式和复数形式的手性 Plebański 公式中定义 所以（3） 联系。在这些理论中，就像在度量公式中的类似物一样，宇宙常数不采用规定值，而是积分常数，其值在不同（经典）解之间可能不同。我们讨论了在一般复杂的理论中识别洛伦兹解时的一些微妙之处，并展示了如何将这些理论简化为类似于克拉斯诺夫广义相对论的纯联系形式主义的“纯联系”形式。