We consider three-dimensional (3D) lattice SU⁡(𝑁𝑐) gauge Higgs theories with multicomponent (𝑁𝑓>1) degenerate scalar fields and 𝑈⁡(𝑁𝑓) global symmetry, focusing on systems with 𝑁𝑐=2, to identify critical behaviors that can be effectively described by the corresponding 3D SU⁡(𝑁𝑐) gauge Higgs field theory. The field-theoretical analysis of the RG flow allows one to identify a stable charged fixed point for large values of 𝑁𝑓, that would control transitions characterized by the global symmetry-breaking pattern U⁡(𝑁𝑓)→SU⁡(2)⊗U⁡(𝑁𝑓−2). Continuous transitions with the same symmetry-breaking pattern are observed in the SU(2) lattice gauge model for 𝑁𝑓≥30. Here we present a detailed finite-size scaling analysis of the Monte Carlo data for several large values of 𝑁𝑓. The results are in substantial agreement with the field-theoretical predictions obtained in the large-𝑁𝑓 limit. This provides evidence that the SU⁡(𝑁𝑐) gauge Higgs field theories provide the correct effective description of the 3D large-𝑁𝑓 continuous transitions between the disordered and the Higgs phase, where the flavor symmetry breaks to SU⁡(2)⊗U⁢(𝑁𝑓−2). Therefore, at least for large enough 𝑁𝑓, the 3D SU⁡(𝑁𝑐) gauge Higgs field theories with multicomponent scalar fields can be nonperturbatively defined by the continuum limit of lattice discretized models with the same local and global symmetries.

中文翻译：

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三维晶格 SU（Nc）规范 Higgs 模型的带电临界行为和非扰动连续极限


我们考虑了具有多分量 （Nf>1） 简并标量场和 U（Nf） 全局对称性的三维 （3D） 晶格 SU（Nc） 规范希格斯理论，重点关注 Nc=2 的系统，以确定可以由相应的 3D SU（Nc） 有效描述的关键行为规范希格斯场论。RG 流的场论分析允许人们确定大值 Nf 的稳定带电固定点，这将控制以全局对称性破坏模式 U（Nf）→SU（2）⊗U（Nf-2） 为特征的跃迁。在 Nf≥30 的 SU（2） 晶格规范模型中观察到具有相同对称破坏模式的连续跃迁。在这里，我们提供了 Nf 的几个大值的蒙特卡洛数据的详细有限尺寸缩放分析。结果与在大 Nf 极限中获得的场论预测基本一致。这提供了证据，证明 SU（Nc） 规范希格斯场论提供了无序相和希格斯相之间的 3D 大 Nf 连续过渡的正确有效描述，其中风味对称性打破为 SU（2）⊗U（Nf−2）。因此，至少对于足够大的 Nf，具有多分量标量场的 3D SU（Nc） 规范希格斯场论可以由具有相同局部和全局对称性的晶格离散模型的连续体极限非扰动定义。