从规范线性西格玛模型到$\mathbb{WCP}(N,\tilde{N})$的二维几何表示
From Gauged Linear Sigma Models to Geometric Representation of $\mathbb{WCP}(N,\tilde{N})$ in 2D
摘要：
在本文中，两个问题得到解决。首先，我们讨论了一类规范线性西格玛模型（GLSM）在低能极限下约化为$\mathbb{WCP}(N,\tilde{N})$非线性西格玛模型（NLSM）的重整化性质。有时，他们被称为Hanany-Tong模型。如果超对称性是${\cal N} =(2,2)$的紫外发散对数在LGSM出现，在Fayet-Iliopoulos参数的重整化，并用尽了一个单一的蝌蚪图。在子NLSM中情况并非如此。因此，在GLSM和他们的子NLSM的单圈重正化是不同的，我们解释了这种差异，并确定其来源。特别是，我们表明，为什么在$N=\tilde N$有没有在父GLSM中的紫外线照射，而它们出现在相应的NLSM不消失。在本文的第二部分中，我们讨论了同样的问题，为一类${\cal N} =(0,2)$ GLSM考虑以前。在这种情况下，重正化不限于一个循环; GLSM的所有阶精确$β$函数是已知的。我们讨论发散循环在一个和两个循环的水平。
英文摘要：
In this paper two issues are addressed. First, we discuss renormalization properties of a class of gauged linear sigma models (GLSM) which reduce to $\mathbb{WCP}(N,\tilde{N})$ non-linear sigma models (NLSM) in the low-energy limit. Sometimes they are referred to as the Hanany-Tong models. If supersymmetry is ${\cal N} =(2,2)$ the ultraviolet-divergent logarithm in LGSM appears, in the renormalization of the Fayet-Iliopoulos parameter, and is exhausted by a single tadpole graph. This is not the case in the daughter NLSMs. As a result, the one-loop renormalizations are different in GLSMs and their daughter NLSMs We explain this difference and identify its source. In particular, we show why at $N=\tilde N$ there is no UV logarithms in the parent GLSM, while they do appear on the corresponding NLSM does not vanish. In the second part of the paper we discuss the same problem for a class of ${\cal N} =(0,2)$ GLSMs considered previously. In this case renormalization is not limited to one loop; all-orders exact $β$ functions for GLSMs are known. We discuss divergent loops at one and two-loop levels.
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