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arXiv 1502.05976hep-th
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超对称性、边界作用和膜荷

On Supersymmetry, Boundary Actions and Brane Charges

Lorenzo Di Pietro, Nizan Klinghoffer, Itamar Shamir

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31 pages, 1 figure
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摘要：

超对称变换将拉格朗日$\mathscr{L}$变为全导数$δ\mathscr{L} = \partial_μ\mathcal{V}^μ$。在有边界的流形上，全导数项是保持超对称性的障碍。这种全导项可以通过边界作用量抵消，而无需指定边界条件，但仅适用于超对称子代数。我们研究补偿边界行动$\mathcal{N}=1$超对称性在4D，并表明，它们是独立的理论和边界条件的细节确定。存在两种不同的边界作用，它们对应于保持相反手性的超荷的线性组合（称为A型）或独立地保持相反手性的超荷（B型）。第一个选择保留了一个同构于$\mathcal{N} = 1$的3d子代数，而第二个选择只保留了洛伦兹对称的2d子群和一个同构于$\mathcal{N} = (0,2)$的2d子代数。这些子代数与半BPS对象一一对应：A型对应于域壁，而B型对应于弦。我们表明，整合的完整的电流代数，并考虑到边界的贡献导致一个能量动量张量，其中包含边界项。在这两种情况下，边界项分别来自畴壁电流和弦电流。

英文摘要：

Supersymmetry transformations change the Lagrangian $\mathscr{L}$ into a total derivative $δ\mathscr{L} = \partial_μ\mathcal{V}^μ$. On manifolds with boundaries the total derivative term is an obstruction to preserving supersymmetry. Such total derivative terms can be canceled by a boundary action without specifying boundary conditions, but only for a subalgebra of supersymmetry. We study compensating boundary actions for $\mathcal{N}=1$ supersymmetry in 4d, and show that they are determined independently of the details of the theory and of the boundary conditions. Two distinct classes of boundary actions exist, which correspond to preserving either a linear combination of supercharges of opposite chirality (called A-type) or supercharges of opposite chirality independently (B-type). The first option preserves a subalgebra isomorphic to $\mathcal{N} = 1$ in 3d, while the second preserves only a 2d subgroup of the Lorentz symmetry and a subalgebra isomorphic to $\mathcal{N} = (0,2)$ in 2d. These subalgebras are in one to one correspondence with half-BPS objects: the A-type corresponds to domain walls while the B-type corresponds to strings. We show that integrating the full current algebra and taking into account boundary contributions leads to an energy-momentum tensor which contains the boundary terms. The boundary terms come from the domain wall and string currents in the two respective cases.

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