arXiv 1607.007262016-07-04hep-th

Frobenius-Chern-Simons规范理论

Frobenius-Chern-Simons gauge theory

Roberto Bonezzi, Nicolas Boulanger, Ergin Sezgin, Per Sundell

备注：: 44 pages
DOI：: 10.1088/1751-8121/50/5/055401

摘要：

给定取值于内部结合代数H的奇维非交换流形上的一组微分形式，我们证明了最一般的三次协变Hamilton作用量（不含质量项）是由具有分次对称非退化双线性形式的Z_2-分次结合代数F控制的.这类模型提供了Frobenius-Chern-Simons模型（FCS）的自然推广，该模型在arXiv：1505.04957中提出，作为最小玻色子四维高自旋引力理论的离壳公式。如果F是酉的，并且Z_2-分次是从一个在真Frobenius子代数外的Klein算子导出的，那么作用量可以用一个值为H和F的直积的超联络写成类似于拓扑开弦场论的形式.我们基于C[Z_2 x Z_4]的扭曲给出了这类新模型，它导致AdS_4上的自对偶复化规范场.若F是3阶的，则FCS模型可以对壳上的零形约束一致截断。其中两个例子是C[（Z_2）^3]的扭曲，它产生了原始模型，以及Clifford代数Cl_2n，它提供了具有规范代数hu（4^{n-1}，0）的玻色子Konstein-Vasiliev模型的FCS公式。

英文摘要：

Given a set of differential forms on an odd-dimensional noncommutative manifold valued in an internal associative algebra H, we show that the most general cubic covariant Hamiltonian action, without mass terms, is controlled by an Z_2-graded associative algebra F with a graded symmetric nondegenerate bilinear form. The resulting class of models provide a natural generalization of the Frobenius-Chern-Simons model (FCS) that was proposed in arXiv:1505.04957 as an off-shell formulation of the minimal bosonic four-dimensional higher spin gravity theory. If F is unital and the Z_2-grading is induced from a Klein operator that is outer to a proper Frobenius subalgebra, then the action can be written on a form akin to topological open string field theory in terms of a superconnection valued in the direct product of H and F. We give a new model of this type based on a twisting of C[Z_2 x Z_4], which leads to self-dual complexified gauge fields on AdS_4. If F is 3-graded, the FCS model can be truncated consistently as to zero-form constraints on-shell. Two examples thereof are a twisting of C[(Z_2)^3] that yields the original model, and the Clifford algebra Cl_2n which provides an FCS formulation of the bosonic Konstein--Vasiliev model with gauge algebra hu(4^{n-1},0).

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