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arXiv 1306.3407hep-thmath-phmath.MP
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自对偶超对称非线性西格玛模型

Self-dual supersymmetric nonlinear sigma models

S. M. Kuzenko, I. N. McArthur

备注：
22 pages; V2: typos corrected
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摘要：

在四维N=1 Minkowski超空间中，一般的四维目标空间非线性西格玛模型可以用CCL（chiral and complex linear）动力学变量来实现，CCL动力学变量由一个手征标量、一个复线性标量及其共轭超场组成.在这里，我们介绍了CCL西格玛模型，是在U（1）“对偶旋转”交换动力学变量和他们的运动方程不变。这种西格玛模型的拉格朗日量证明服从一个偏微分方程，该偏微分方程类似于非线性电动力学的U（1）对偶不变模型所服从的自对偶方程。这些西格玛模型在勒让德变换下是自对偶的，勒让德变换同时将（i）手性多重峰对偶为复线性多重峰;以及（ii）复线性多重峰对偶为手性多重峰。任何CCL西格玛模型都有一个由两个手征多重峰给出的对偶公式。CCL西格玛模型的U（1）对偶不变性在对偶手征公式中被证明等价于旋转两个手征标量的明显U（1）不变性。由于目标空间有一个全纯基灵矢量，西格玛模型拥有第三个配方实现的手征多重和张量多重。U（1）对偶不变CCL西格玛模型族包含N=2超对称理论的子集。它们的目标空间是具有非零Killing向量场的超Kahler流形。在Killing矢量场是三全纯的情况下，西格玛模型允许一个关于自相互作用的离壳N=2张量多重态的对偶公式。我们还确定了一个子集的CCL西格玛模型，这是在一个一对一的对应关系的U（1）对偶不变模型的非线性电动力学。这些西格玛模型的目标空间等距组包含一个子群U（1）x U（1）。

英文摘要：

In four-dimensional N=1 Minkowski superspace, general nonlinear sigma models with four-dimensional target spaces may be realised in term of CCL (chiral and complex linear) dynamical variables which consist of a chiral scalar, a complex linear scalar and their conjugate superfields. Here we introduce CCL sigma models that are invariant under U(1) "duality rotations" exchanging the dynamical variables and their equations of motion. The Lagrangians of such sigma models prove to obey a partial differential equation that is analogous to the self-duality equation obeyed by U(1) duality invariant models for nonlinear electrodynamics. These sigma models are self-dual under a Legendre transformation that simultaneously dualises (i) the chiral multiplet into a complex linear one; and (ii) the complex linear multiplet into a chiral one. Any CCL sigma model possesses a dual formulation given in terms of two chiral multiplets. The U(1) duality invariance of the CCL sigma model proves to be equivalent, in the dual chiral formulation, to a manifest U(1) invariance rotating the two chiral scalars. Since the target space has a holomorphic Killing vector, the sigma model possesses a third formulation realised in terms of a chiral multiplet and a tensor multiplet. The family of U(1) duality invariant CCL sigma models includes a subset of N=2 supersymmetric theories. Their target spaces are hyper Kahler manifolds with a non-zero Killing vector field. In the case that the Killing vector field is triholomorphic, the sigma model admits a dual formulation in terms of a self-interacting off-shell N=2 tensor multiplet. We also identify a subset of CCL sigma models which are in a one-to-one correspondence with the U(1) duality invariant models for nonlinear electrodynamics. The target space isometry group for these sigma models contains a subgroup U(1) x U(1).

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