The exotic \(\mathcal{N} = (3,1)\) and \(\mathcal{N} = (4,0)\) supergravity theories in six dimensions are theories describing potentials with mixed-symmetry indices satisfying a second order self-duality relation, and giving rise to maximal supergravity in five dimensions upon dimensional reduction. After reviewing how the linearised equations are constructed, we show how introducing additional gauge symmetries one can derive the same equations from first-order self-duality relations. We discuss how this result can be used to obtain a covariant lagrangian.

中文翻译：

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论异域六维超重力理论

六个维度上的奇异\（\ mathcal {N} =（3,1）\）和\（\ mathcal {N} =（4,0）\）超重力理论是描述具有混合对称指数满足第二个势的势的理论阶自对偶关系，并在降维时在五个维度上产生最大超重力。在回顾了线性方程组的构造方式之后，我们展示了如何引入额外的量规对称性可以从一阶自对偶关系中导出相同的方程组。我们讨论如何将此结果用于获得协变拉格朗日。