arXiv 1208.45332012-08-20hep-th

自对偶Yang-Mills和向量旋量场、幂零费米子对称性和超对称可积系统

Self-Dual Yang-Mills and Vector-Spinor Fields, Nilpotent Fermionic Symmetry, and Supersymmetric Integrable Systems

Hitoshi Nishino, Subhash Rajpoot

备注：: 15 pages, no figures
DOI：: 10.1103/PhysRevD.86.065012

摘要：

我们提出了一个2+2维的自对偶杨-米尔斯场和一个具有幂零费米子对称性（但不是超对称性）的自对偶矢量-旋量场的系统，它产生了低维的超对称可积系统.我们的场容量是（A_μ^I，λ_μ^I，χ^{I J}），其中I和J是任意规范群的伴随指数. X ^{IJ}是一致性的Stueckelberg域。该系统具有局部幂零费米子对称性，代数N_α^I，N_β^J = 0.通过适当的降维，该系统生成了D=2+1的超对称Kadomtsev-Petviashvili方程和D=1+1的超对称Korteweg-de Vries方程.我们还表明，一个类似的自对偶系统在七个维度产生自对偶系统在四个维度。基于我们的结果，我们推测，低维超对称积分模型可以由高维非超对称自对偶系统生成，只有幂零费米子对称性。

英文摘要：

We present a system of a self-dual Yang-Mills field and a self-dual vector-spinor field with nilpotent fermionic symmetry (but not supersymmetry) in 2+2 dimensions, that generates supersymmetric integrable systems in lower dimensions. Our field content is (A_μ^I, ψ_μ^I, χ^{I J}), where I and J are the adjoint indices of arbitrary gauge group. The χ^{I J} is a Stueckelberg field for consistency. The system has local nilpotent fermionic symmetry with the algebra \{N_α^I, N_β^J \} = 0. This system generates supersymmetric Kadomtsev-Petviashvili equations in D=2+1, and supersymmetric Korteweg-de Vries equations in D=1+1 after appropriate dimensional reductions. We also show that a similar self-dual system in seven dimensions generates self-dual system in four dimensions. Based on our results we conjecture that lower-dimensional supersymmetric integral models can be generated by non-supersymmetric self-dual systems in higher dimensions only with nilpotent fermionic symmetries.

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摘要：

英文摘要：

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