Endrődi G, Kovács T G, Markó G
Fakultät für Physik, Universität Bielefeld, D-33615 Bielefeld, Germany.
Eötvös Loránd University, Pázmány Péter sétány 1/A, H-1117 Budapest Hungary.
Phys Rev Lett. 2021 Dec 3;127(23):232002. doi: 10.1103/PhysRevLett.127.232002.
We discuss spontaneously broken quantum field theories with a continuous global symmetry group via the constraint effective potential. Employing lattice simulations with constrained values of the order parameter, we demonstrate explicitly that the path integral is dominated by inhomogeneous field configurations and that these are unambiguously related to the flatness of the effective potential in the broken phase. We determine characteristic features of these inhomogeneities, including their topology and the scaling of the associated excess energy with their size. Concerning the latter we introduce the differential surface tension-the generalization of the concept of a surface tension pertaining to discrete symmetries. Within our approach, spontaneous symmetry breaking is captured merely via the existence of inhomogeneities, i.e., without the inclusion of an explicit breaking parameter and a careful double limiting procedure to define the order parameter. While here we consider the three-dimensional O(2) model, we also elaborate on possible implications of our findings for the chiral limit of QCD.
我们通过约束有效势来讨论具有连续全局对称群的自发破缺量子场论。利用序参量具有约束值的晶格模拟，我们明确证明路径积分由非均匀场构型主导，并且这些构型与破缺相中有效势的平坦性明确相关。我们确定了这些非均匀性的特征，包括它们的拓扑结构以及相关多余能量随其尺寸的标度。关于后者，我们引入了微分表面张力——这是与离散对称性相关的表面张力概念的推广。在我们的方法中，自发对称破缺仅通过非均匀性的存在来体现，即无需引入明确的破缺参数以及定义序参量的精细双极限过程。虽然这里我们考虑三维O(2)模型，但我们也阐述了我们的发现对量子色动力学手征极限的可能影响。
