arXiv 1406.76022014-06hep-th

SU（4）调和超空间与超对称规范理论

SU(4) harmonic superspace and supersymmetric gauge theory

B. M. Zupnik

备注：: 21 pages, v2: corrected version
DOI：: 10.1007/s11232-015-0322-y

摘要：

我们考虑的调和超空间形式主义的$N=4$超对称使用的$SU(4)/SU(2)\times SU(2)\times U(1)$谐波，这是早期应用到阿贝尔规范理论。标准超空间中的N=4非阿贝尔约束被重新表述为两个基本解析超场的调和超空间方程：1维的独立超场强度W和无量纲调和规范4-预势V，其$U(1)$荷为2。这些约束方程I显然依赖于格拉斯曼坐标$θ$，尽管它们在不寻常的N=4超对称变换下是协变的。本文分析了两个无约束非交换解析超场W和V的超规范理论的一种替代调和形式。在这种形式中，规范不变作用量A（W，V）在每一项中都包含$θ$因子，它在$SU(4)$自同构群下是不变的。在该模型中，两个无限维N=4超多重态与物理场和辅助场的相互作用出现在分量场的水平上。作用量A（W，V）生成运动解析方程II，替代谐波-超空间超场约束I。这两组方程给出了$N=4$规范超多重态的物理分量场的等价方程，它们连接了两个超场的辅助场和物理场。构造了阿贝尔谐振子超场W的非线性有效相互作用。

英文摘要：

We consider the harmonic-superspace formalism in the $N=4$ supersymmetry using the $SU(4)/SU(2)\times SU(2)\times U(1)$ harmonics which was earlier applied to the abelian gauge theory. The N=4 non-abelian constraints in a standard superspace are reformulated as the harmonic-superspace equations for two basic analytic superfields: the independent superfield strength W of a dimension 1 and the dimensionless harmonic gauge 4-prepotential V having the $U(1)$ charge 2. These constraint equations I manifestly depend on the Grassmann coordinates $θ$, although they are covariant under the unusual N=4 supersymmetry transformations. We analyze an alternative harmonic formalism of the supergauge theory for two unconstrained nonabelian analytic superfields W and V. The gauge-invariant action A(W,V) in this formalism contains $θ$ factors in each term, it is invariant under the $SU(4)$ automorphism group. In this model, the interaction of two infinite-dimensional N=4 supermultiplets with the physical and auxiliary fields arises at the level of component fields. The action A(W,V) generate analytic equations of motion II alternative to the harmonic-superspace superfield constraints I. Both sets of equations give us the equivalent equations for the physical component fields of the $N=4$ gauge supermultiplet, they connect auxiliary and physical fields of two superfields. The nonlinear effective interaction of the abelian harmonic superfield W is constructed.

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