Bootstrapping the O(N) archipelago

By Filip Kos, David Poland, David Simmons-Duffin, A. Vichi. 2015

238 citations recorded by the source corpus.

A bstractWe study 3d CFTs with an O(N) global symmetry using the conformal bootstrap for a system of mixed correlators. Specifically, we consider all nonvanishing scalar four-point functions containing the lowest dimension O(N) vector ϕi and the lowest dimension O(N) singlet s, assumed to be the only relevant operators in their symmetry representations. The constraints of crossing symmetry and unitarity for these four-point functions force the scaling dimensions (Δϕ, Δs) to lie inside small islands. We also make rigorous determinations of current two-point functions in the O(2) and O(3) models, with applications to transport in condensed matter systems.

Subfields: Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/c44d9da166f11d277029bda469a51888faab446d

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Citations in the corpus

On the CFT operator spectrum at large global charge (2015, methodology): “Also, much recent progress has been made on the conformal bootstrap both for the three-dimensional critical O(N) models and the O(2) model, specifically [13], as well as for the W = Φ3 theory [31, 32], and it would be desirable to see how such analytic bootstrap methods may confirm and/or complement”
The ϵ ?> -expansion from conformal field theory (2015, background): “Many other conformal theories, such as the O(N) model [21, 22], models with supersymmetry in various dimensions [23–32], as well as other less familiar or conjectural conformal theories [33–39] are being studied.”
EPFL Lectures on Conformal Field Theory in D ≥ 3 Dimensions (2016, methodology): “This happens for the 3d Ising model [46, 47] and for the O(N) models [48].”
Carving out OPE space and precise O(2) model critical exponents (2019, methodology): “In favorable circumstances, such exclusion plots contain small islands around the theory of interest — we then say that we have “isolated” the theory [5–9].”
A proof of the conformal collider bounds (2016, unknown): “[2–5, 61–72]).”
An algebraic approach to the analytic bootstrap (2015, methodology): “We hope that we can check this statement using the results obtained by other methods in the near future [16, 17].”
Bootstrapping 3D fermions (2015, methodology): “This method achieved an impressive degree of success, for example, by enabling accurate determinations of the dimensions of low-lying operators in particular CFTs, such as the 3D Ising [5–8] and critical O(N) vector [9, 10] models.”
Bounding the space of holographic CFTs with chaos (2016, background): “On the other hand, in looking at examples of 3d CFTs with ∆ < 1 scalars – the Ising model, critical Gross-Neveu model, and all O(N) models with exactly one relevant scalar in each of the O(N) singlet and vector representations [126] – such exchanges do not appear in the OPE of identical operators.”