We discuss the formulation of cosmological topologically massive (simple) supergravity theory in three-dimensional Riemann-Cartan space-times. We use the language of exterior differential forms and the properties of Majorana spinors on 3-dimensional space-times to explicitly demonstrate the local supersymmetry of the action density involved. Exact coupled field equations that are complete in both of their bosonic and fermionic sectors are derived by a first order variational principle subject to a torsion-constraint imposed by the method of Lagrange multipliers. Cotton and Cottino 2-forms that are complete to all orders in the gravitino field are derived and their properties such as trace are investigated.

中文翻译：

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宇宙拓扑大质量超引力变分场方程

我们讨论了三维 Riemann-Cartan 时空中宇宙学拓扑质量（简单）超引力理论的公式。我们使用外微分形式的语言和马约拉纳旋量在 3 维时空上的性质来明确证明所涉及的动作密度的局部超对称性。在它们的玻色子和费米子扇区中都完整的精确耦合场方程是通过一阶变分原理推导出来的，该原理受到拉格朗日乘子方法施加的扭力约束。推导了对重力场中所有阶都完备的 Cotton 和 Cottino 2-形式，并研究了它们的性质，如迹。