线性规范对称性破缺下的格点规范理论
Lattice gauge theories in the presence of a linear gauge-symmetry breaking
摘要：
研究了三维标量场格点规范理论中的规范对称性破缺微扰效应。我们研究这个问题的过渡中，规范相关性不是关键的，规范对称性只选择规范不变的标量自由度，成为关键。实现这种行为的范例模型是格点CP（1）模型，或者更一般地，具有双分量复标量场和紧致规范场的格点阿贝尔-希格斯模型。我们认为这个模型中存在的线性GSB扰动。规范对称性对于GSB扰动是相当鲁棒的：在有限小GSB项的存在下，连续极限也是规范不变的。我们还确定了该模型的相图。它有一个无序相和两个相，分别是张量和矢量有序。它们被连续的过渡线分开，这些过渡线属于O（3），O（4）和O（2）向量普适类，并在多临界点相遇。我们注意到，CP（1）规范对称临界点的行为与规范关联变得临界的跃迁有很大不同，例如在非紧格点阿贝尔-希格斯模型中由带电不动点控制的跃迁：在这种情况下，行为对GSB扰动非常敏感。
英文摘要：
We study the effects of gauge-symmetry breaking (GSB) perturbations in three-dimensional lattice gauge theories with scalar fields. We study this issue at transitions in which gauge correlations are not critical and the gauge symmetry only selects the gauge-invariant scalar degrees of freedom that become critical. A paradigmatic model in which this behavior is realized is the lattice CP(1) model or, more generally, the lattice Abelian-Higgs model with two-component complex scalar fields and compact gauge fields. We consider this model in the presence of a linear GSB perturbation. The gauge symmetry turns out to be quite robust with respect to the GSB perturbation: the continuum limit is gauge-invariant also in the presence of a finite small GSB term. We also determine the phase diagram of the model. It has one disordered phase and two phases that are tensor and vector ordered, respectively. They are separated by continuous transition lines, which belong to the O(3), O(4), and O(2) vector universality classes, and which meet at a multicritical point. We remark that the behavior at the CP(1) gauge-symmetric critical point substantially differs from that at transitions in which gauge correlations become critical, for instance at transitions in the noncompact lattice Abelian-Higgs model that are controlled by the charged fixed point: in this case the behavior is extremely sensitive to GSB perturbations.
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