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arXiv 1306.1115hep-th
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基于陪集方法的超对称分量作用

Supersymmetric component actions via coset approach

S. Bellucci, S. Krivonos, A. Sutulin

备注：
12 pages, PACS: 11.30.Pb, 12.60.Jv
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摘要：

提出了一种在非线性实现（陪集）方法中构造整体超对称性$1/2$部分破缺理论的壳上分量作用量的方法。与标准超场方法中未破缺的超对称性起主导作用相反，我们将注意力转移到自发破缺的超对称性上。结果表明，在一半超对称自发破缺的理论中，所有的物理费米子都是非线性实现的费米子。此外，这些费米子相对于破缺超对称的变换性质与著名的K-Akulov模型相同。正是这一事实完全固定了费米子在分作用量中的所有可能出现：它们只能通过维尔拜因的行列式（以补偿体积形式的变换）和协变导数进入作用量。非常重要的是，在我们的陪集参数化中，其余的物理分量，即所有的玻色子分量，相对于破缺的超对称性变换为“物质场”。显然，在这种情况下，分作用获得了这些“物质场”的阿基洛夫-阿库洛夫作用的形式。作用量的完全形式可以通过两个额外的要求进一步确定：a）再现玻色子极限，这在许多有趣的情况下是明确已知的; b）具有适当的线性化形式，它必须相对于线性化的未破缺超对称性不变。我们提供一般的考虑，通过一个详细的例子，$N=1$超膜的组成部分的行动，在$D=4$内构建我们的程序。在这种情况下，我们提供了准确的证明的不变性的构造组件的作用相对于这两个，破碎和未破碎的超对称。

英文摘要：

We propose a method to construct the on-shell component actions for the theories with $1/2$ partial breaking of global supersymmetry within the nonlinear realization (coset) approach. In contrast with the standard superfield approach in which unbroken supersymmetry plays the leading role, we have shifted the attention to the spontaneously broken supersymmetry. It turns out that in the theories in which half of supersymmetries is spontaneously broken, all physical fermions are just the fermions of the nonlinear realization. Moreover, the transformation properties of these fermions with respect to the broken supersymmetry are the same as in the famous Volkov-Akulov model. Just this fact completely fixed all possible appearances of the fermions in the component action: they can enter the action through the determinant of the vielbein (to compensate the transformation of the volume form) and the covariant derivatives, only. It is very important that in our parametrization of the coset the rest of physical components, i.e. all bosonic components, transform as ``matter fields'' with respect to the broken supersymmetry. Clearly, in such a situation the component action acquires the form of the Volkov-Akulov action for these ``matter fields''. The complete form of the action can be further fixed by two additional requirements: a) to reproduce the bosonic limit, which is explicitly known in many interesting cases, and b) to have a proper linearized form, which has to be invariant with respect to the linearized unbroken supersymmetry. We supply the general consideration by a detailed example of the component action of $N=1$ supermembrane in $D=4$ constructed within our procedure. In this case we provide the exact proof of the invariance of the constructed component action with respect to both, broken and unbroken supersymmetries.

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