SQED中半局部弦世界片上的异质变形西格玛模型
Heterotically Deformed Sigma Models on the World Sheet of Semilocal Strings in SQED
摘要：
一个新的二维$\mathcal{N}=(0,2)$超对称非线性西格玛模型描述了四维$\mathcal{N}=2$ SQED中BPS半局域涡弦的内模量动力学。虽然这些弦的核心与Abrikosov-Nielsen-Olesen涡旋非常相似，但它们被定义为具有特征尺寸模量，非常像瞬子块尺寸。这意味着涡旋的组成场不会随着远离弦的核心而指数衰减，而是作为有理函数衰减。令人惊讶的是，问题中额外尺度的出现也允许为BPS方程写出显式的、解析的、近似的解。尽管半定域涡旋和非阿贝尔涡旋在概念上有很大的差异，但它们的模结构似乎有一个主要的共同特征，即当超对称破缺势项加入时空理论时，它们都经历了相同的杂化变形，从$\mathcal{N}=2$移动到$\mathcal{N}=1$。通过为规范标量多重态增加一个质量项，在世界片上产生了一种异质变形，通过将超平移的费米子零模耦合到超尺寸模上，将超对称性打破到$(0,2)$。两个不同扇区的零模之间的这种相互作用已经被假设，随后在非阿贝尔弦中被发现，提供了一种巧妙的方法来绕过通过祖米诺定理偶然的超对称性增强。我们发现，对于小值的时空质量项，一个完全类似的长期开发的世界表的半本地字符串。
英文摘要：
A new two dimensional $\mathcal{N}=(0,2)$ Supersymmetric Non-Linear Sigma Model describes the dynamics of internal moduli of the BPS semi-local vortex string supported in four dimensional $\mathcal{N}=2$ SQED. While the core of these strings is very similar to Abrikosov-Nielsen-Olesen vortices, they are defined with a characteristic size modulus, much like the instanton lump size. This entails that the constituting fields of the vortex do not decay exponentially, as one goes far away from the core of the string, but as a rational function. The appearance of an extra scale in the problem also allows for an explicit, analytic, approximate solution to be written for the BPS equation, surprisingly. Despite the conceptually large differences between semi-local and non-Abelian vortices, it appears that the moduli structures have one main common feature, both undergo the same kind of heterotic deformation when a supersymmetry breaking potential term is added to the spacetime theory, moving from $\mathcal{N}=2$ to $\mathcal{N}=1$. By adding a mass term for the gauge scalar multiplet, a heterotic deformation develops on the worldsheet, which breaks supersymmetry down to $(0,2)$ by coupling supertranslational fermionic zero modes to supersize ones. Such an interaction between zero modes of two different sectors was already hypothesized and subsequently found for non-Abelian strings, providing a neat way of circumventing accidental supersymmetry enhancement via Zumino's theorem. We find that, for small values of the spacetime mass term, an entirely analogous term develops on the worldsheet of semi-local strings.
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