We consider two-dimensional lattice SU(N_c) gauge theories with N_f real scalar fields transforming in the adjoint representation of the gauge group and with a global O(N_f) invariance. Focusing on systems with N_f ≥ 3, we study their zero-temperature limit, to understand under which conditions a continuum limit exists, and to investigate the nature of the associated quantum field theory. Extending previous analyses, we address the role that the gauge-group representation and the quartic scalar potential play in determining the nature of the continuum limit (when it exists). Our results further corroborate the conjecture that the continuum limit of two-dimensional lattice gauge models with multiflavor scalar fields, when it exists, is associated with a σ model defined on a symmetric space that has the same global symmetry as the lattice model.

我们考虑二维晶格SU（N _c）规范理论，其中N _f个实标量场在规范组的伴随表示中变换，并且具有全局O（N _f）不变性。集中在与系统Ñ _˚F ≥3，我们研究了它们的零温度极限，以了解在什么条件下存在连续极限，并研究了相关量子场理论的性质。扩展先前的分析，我们讨论量规组表示和四次标量势在确定连续极限（如果存在）的性质中所起的作用。我们的结果进一步证实了这样的猜想，即带有多味标量场的二维晶格规模型的连续极限存在时，它与在与晶格模型具有相同整体对称性的对称空间上定义的σ模型相关联。