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arXiv 0809.2684hep-th
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Seiberg-Witten映射与超对称性

The Seiberg-Witten map and supersymmetry

C. P. Martin, C. Tamarit

备注：
28 pages. No figures
发表信息：
JHEP0811:087,2008
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摘要：

U（1）向量超场的一阶homegamn Seiberg-Witten（SW）映射方程缺乏局部解，迫使我们求出这些方程的最一般解，即在普通向量超场v、它的手征和反手征投影以及它们的susy协变导数中的二次多项式.利用这个解，我们构造了非对易U（1）SYM的一个普通对偶，它是关于N=1的susy代数的一个线性表示的普通域.利用N=1 U（1）规范超多重态的标准SW映射，我们定义了一个普通U（1）规范理论，它是WZ规范中非对易U（1）SYM的对偶.我们表明，这样得到的普通对偶是超对称的，因为我们证明，我们去，普通规范和费米子领域，我们用来定义它进行非线性表示的N=1 susy代数。最后我们证明了上述两个非对易U（1）SYM的普通规范理论实际上是同一个N=1 susy规范理论。我们还表明，在本文中，标准的SW地图从来没有的θ θ-酒吧分量的局部超场在v和检查，至少在一个给定的近似，一个合适的字段重新定义的地图，使非交换和普通的-在一个BMN字段- susy U（1）DBI行动等价。

英文摘要：

The lack of any local solution to the first-order-in-h omegamn Seiberg-Witten (SW) map equations for U(1) vector superfields compels us to obtain the most general solution to those equations that is a quadratic polynomial in the ordinary vector superfield, v, its chiral and antichiral projections and the susy covariant derivatives of them all. Furnished with this solution, which is local in the susy Landau gauge, we construct an ordinary dual of noncommutative U(1) SYM in terms of ordinary fields which carry a linear representation of the N=1 susy algebra. By using the standard SW map for the N=1 U(1) gauge supermultiplet we define an ordinary U(1) gauge theory which is dual to noncommutative U(1) SYM in the WZ gauge. We show that the ordinary dual so obtained is supersymmetric, for, as we prove as we go along, the ordinary gauge and fermion fields that we use to define it carry a nonlinear representation of the N=1 susy algebra. We finally show that the two ordinary duals of noncommutative U(1) SYM introduced above are actually the same N=1 susy gauge theory. We also show in this paper that the standard SW map is never the theta theta--bar component of a local superfield in v and check that, at least at a given approximation, a suitable field redefinition of that map makes the noncommutative and ordinary --in a Bmn field-- susy U(1) DBI actions equivalent.

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