Bonezzi Roberto, Hohm Olaf
Institute for Physics, Humboldt University Berlin, Zum Großen Windkanal 6, D-12489 Berlin, Germany.
Commun Math Phys. 2021;382(1):277-315. doi: 10.1007/s00220-021-03973-8. Epub 2021 Feb 18.
The gauge theories underlying gauged supergravity and exceptional field theory are based on tensor hierarchies: generalizations of Yang-Mills theory utilizing algebraic structures that generalize Lie algebras and, as a consequence, require higher-form gauge fields. Recently, we proposed that the algebraic structure allowing for consistent tensor hierarchies is axiomatized by 'infinity-enhanced Leibniz algebras' defined on graded vector spaces generalizing Leibniz algebras. It was subsequently shown that, upon appending additional vector spaces, this structure can be reinterpreted as a differential graded Lie algebra. We use this observation to streamline the construction of general tensor hierarchies, and we formulate dynamics in terms of a hierarchy of first-order duality relations, including scalar fields with a potential.
它是杨-米尔斯理论的推广，利用了推广李代数的代数结构，因此需要高阶形式的规范场。最近，我们提出允许一致张量层次结构的代数结构由定义在推广莱布尼茨代数的分次向量空间上的“无穷增强莱布尼茨代数”进行公理化。随后表明，在附加额外的向量空间后，这种结构可以重新解释为一个微分分次李代数。我们利用这一观察结果简化了一般张量层次结构的构建，并根据一阶对偶关系层次来表述动力学，包括具有势的标量场。
