Bonati Claudio, Franchi Alessio
Dipartimento di Fisica dell'Università di Pisa and INFN, Largo Pontecorvo 3, I-56127 Pisa, Italy.
Phys Rev E. 2022 May;105(5-1):054117. doi: 10.1103/PhysRevE.105.054117.
We address the interplay between local and global symmetries in determining the continuum limit of two-dimensional lattice scalar theories characterized by SO(N_{c}) gauge symmetry and non-Abelian O(N_{f}) global invariance. We argue that, when a quartic interaction is present, the continuum limit of these models corresponds in some cases to the gauged nonlinear σ model field theory associated with the real Grassmannian manifold SO(N_{f})/(SO(N_{c})×SO(N_{f}-N_{c})), which is characterized by the invariance under the color-flavor reflection N_{c}↔N_{f}-N_{c}. Monte Carlo simulations and finite-size scaling analyses, performed for N_{f}=7 and several values of N_{c}, confirm the emergence of the color-flavor reflection symmetry in the scaling limit and support the identification of the continuum limit.
我们研究了局部对称性与全局对称性之间的相互作用，以确定具有(SO(N_{c}))规范对称性和非阿贝尔(O(N_{f}))全局不变性的二维晶格标量理论的连续统极限。我们认为，当存在四次相互作用时，这些模型的连续统极限在某些情况下对应于与实格拉斯曼流形(SO(N_{f})/(SO(N_{c})×SO(N_{f}-N_{c})))相关的规范非线性(\sigma)模型场论，其特征是在色味反射(N_{c}\leftrightarrow N_{f}-N_{c})下的不变性。针对(N_{f}=7)和几个(N_{c})值进行的蒙特卡罗模拟和有限尺寸标度分析，证实了在标度极限中色味反射对称性的出现，并支持对连续统极限的识别。
