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It was recently found that the classical 3d O(N) model in the semi-infinite geometry can exhibit an “extraordinary-log” boundary universality class, where the spin-spin correlation function on the boundary falls off as < S(x) S(0)> ~ 1/ (log x)^q. This universality class exists for a range 2 ≤ N < Nc and Monte-Carlo simulations and conformal bootstrap indicate Nc > 3. In this work, we extend this result to the 3d O(N) model in an infinite geometry with a plane defect. We use renormalization group (RG) to show that in this case the extraordinary-log universality class is present for any finite N ≥ 2. We additionally show, in agreement with our RG analysis, that the line of defect fixed points which is present at infinite N is lifted to the ordinary, special (no defect) and extraordinary-log universality classes by 1/N corrections. We study the “central charge” a for the O(N) model in the boundary and interface geometries and provide a non-trivial detailed check of an a-theorem by Jensen and O’Bannon. Finally, we revisit the problem of the O(N) model in the semi-infinite geometry. We find evidence that at N = Nc the extraordinary and special fixed points annihilate and only the ordinary fixed point is left for N > Nc .
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Effective Geometry, Complexity, and Universality
Post-Wilsonian physics views theories not as isolated points but elements of bigger universality classes, with effective theories emerging in the infrared. This paper makes initial attempts to apply this viewpoint to homogeneous geometries on group manifolds, and complexity geometry in particular. We observe that many homogeneous metrics on low-dimensional Lie groups have markedly different short-distance properties, but nearly identical distance functions at longer distances. Using Nielsen's framework of complexity geometry, we argue for the existence of a large universality class of definitions of quantum complexity, each linearly related to the other, a much finer-grained equivalence than typically considered in complexity theory. We conjecture that at larger complexities, a new effective metric emerges that describes a broad class of complexity geometries, insensitive to various choices of 'ultraviolet' penalty factors. Finally we lay out a broader mathematical program of classifying the effective geometries of right-invariant group manifolds.
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- Award ID(s):
- 2014215
- PAR ID:
- 10352534
- Date Published:
- Journal Name:
- ArXivorg
- Volume:
- arXiv:2111.12700
- ISSN:
- 2331-8422
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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