1. Spontaneous symmetry breaking on surface defects
- Author
-
Cuomo, Gabriel and Zhang, Shuyu
- Subjects
High Energy Physics - Theory ,Condensed Matter - Strongly Correlated Electrons ,High Energy Physics - Theory (hep-th) ,Statistical Mechanics (cond-mat.stat-mech) ,Strongly Correlated Electrons (cond-mat.str-el) ,FOS: Physical sciences ,Condensed Matter - Statistical Mechanics - Abstract
Coleman's theorem states that continuous internal symmetries cannot be spontaneously broken in two-dimensional quantum field theories (QFTs). In this work we consider surface (i.e. two-dimensional) defects in $d$-dimensional conformal field theories (CFTs) invariant under a continuous internal symmetry group $G$. We study under which conditions it is possible for a surface defect to break spontaneously a continuous internal symmetry. We find that spontaneous symmetry breaking (SSB) is disallowed under reasonable assumptions on the defect Renormalization Group (RG) flow. Counterexamples are possible only for exotic RG flows, that do not terminate at a fixed-point. We discuss an example of this kind. We also illustrate the mechanism with which quantum effects prevent SSB for generic defect RG flows. We find a generic weakly coupled defect universality class, where correlation functions decay logarithmically. Our analysis generalizes the recent discovery by Metlitski of the extraordinary-log boundary universality class in the $O(N)$ model., Comment: 37 pages+appendices, 3 figures
- Published
- 2023
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