Color-flavor reflection in the continuum limit of two-dimensional lattice gauge theories with scalar fields.
basic_science · Level V
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- Also identified by DOI 10.1103/PhysRevE.105.054117.
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Abstract
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.