A [Formula: see text] cohomological gravity is introduced. The central piece is a new BRST-like symmetry [Formula: see text] with [Formula: see text] up to a diffeomorphism and gauge symmetry. The only nontrivial observable of this symmetry is a Chern–Simons integral. The construction of the symmetry requires a spin 0 fermion [Formula: see text] and a spin [Formula: see text] boson [Formula: see text] at the minimum, in addition to the standard gravity and gauge fields, to close the algebra off-shell. The gravity action is uniquely determined by requiring a field redefinition type of global symmetry between bosonic and fermionic fields. It is of a simple form [Formula: see text] plus a Chern–Simons term, and appears as the [Formula: see text] supergravity action under a special combination of the fields without independent presence of [Formula: see text] and [Formula: see text]. The [Formula: see text]-invariant path-integral measure, which is also invariant under the global symmetry, is shown to exist for the theory to be valid at quantum level. It achieves only when the fields are redefined under certain combination that is different from the special combination, and the fields in this combination are interpreted as physical fields. At [Formula: see text] limit, where all field combinations converges, the theory reduces to [Formula: see text] supergravity and the global symmetry becomes the local supersymmetry with [Formula: see text] as the local variable. At a nonvanishing [Formula: see text] limit set by residue symmetries upon broken [Formula: see text]-symmetry, the theory admits a cosmological solution that has a wavy term to allow accelerated expansion of the universe while not violate null energy condition.

中文翻译：

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D = 11 中的上同调引力

引入了[公式：见正文]上同调引力。中心部分是一个新的类似 BRST 的对称性 [公式：见文本]，其中 [公式：见文本] 达到微分同胚和规范对称。这种对称性的唯一重要可观测值是陈-西蒙斯积分。对称性的构造至少需要一个自旋 0 的费米子 [公式：见文本] 和一个自旋 [公式：见文本] 玻色子 [公式：见文本]，除了标准重力场和规范场外，以闭合代数脱壳。重力作用是由玻色子和费米子场之间的全局对称场重新定义类型唯一确定的。它是一个简单的形式[公式：见正文]加上一个陈-西蒙斯项，并且在没有独立存在的[公式：见文本]和[公式：见文本]。[公式：见正文]-不变的路径积分测度，在全局对称性下也是不变的，被证明存在，以使该理论在量子水平上有效。它只有在某种不同于特殊组合的组合下重新定义字段，并将该组合中的字段解释为物理字段时才能实现。在所有场组合收敛的[公式：见文本]极限处，理论简化为[公式：见文本]超重力，全局对称变为局部超对称，[公式：见文本]作为局部变量。在一个不消失的[公式：见文本]极限处，由残差对称性在破碎的[公式：见文本]-对称性上设置，