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Navigator Function for the Conformal Bootstrap

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arxiv 2104.09518 v2 pith:FDTUVPGS submitted 2021-04-19 hep-th cond-mat.stat-mech

Marten Reehorst , Slava Rychkov , David Simmons-Duffin , Benoit Sirois , Ning Su , Balt van Rees This is my paper · ORCID
classification hep-thcond-mat.stat-mech
keywords allowedexcludedfunctionnavigatorallowsbootstrapconformalgradient
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Current numerical conformal bootstrap techniques carve out islands in theory space by repeatedly checking whether points are allowed or excluded. We propose a new method for searching theory space that replaces the binary information "allowed"/"excluded" with a continuous "navigator" function that is negative in the allowed region and positive in the excluded region. Such a navigator function allows one to efficiently explore high-dimensional parameter spaces and smoothly sail towards any islands they may contain. The specific functions we introduce have several attractive features: they are everywhere well-defined, can be computed with standard methods, and evaluation of their gradient is immediate due to an SDP gradient formula that we provide. The latter property allows for the use of efficient quasi-Newton optimization methods, which we illustrate by navigating towards the 3d Ising island.

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Cited by 8 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Bootstrapping the 3d Ising Stress Tensor

    hep-th 2024-11 conditional novelty 8.0 of 10

    The mixed σ, ε, T bootstrap gives Δσ = 0.518148806(24), Δε = 1.41262528(29), and new OPE coefficients for the critical 3d Ising CFT.

  2. Descending into the Modular Bootstrap

    hep-th 2026-04 unverdicted novelty 7.0 of 10

    Numerical search finds candidate modular-invariant spectra with integer degeneracies for 1 < c < 8/7 and hints at a stronger gap bound near c = 1.

  3. Bootstrapping Yang-Mills matrix integrals

    hep-th 2025-10 conditional novelty 7.0 of 10

    Bootstrap bounds on ⟨tr XX⟩ and ⟨tr XXXX⟩ in D-matrix Yang-Mills integrals shrink to islands matching Monte Carlo, with large-D trajectories guiding a positivity-free ansatz.

  4. Redundancy Channels in the Conformal Bootstrap

    hep-th 2025-07 conditional novelty 7.0 of 10

    Redundant operators motivate spectral gaps that block accidental symmetry enhancement, yielding the first bootstrap island for the 3D cubic CFT that excludes the O(3) model.

  5. The tricritical Ising CFT and conformal bootstrap

    hep-th 2025-01 conditional novelty 7.0 of 10

    First conformal-bootstrap islands for the tricritical Ising CFT in d=2.5 and d=2.75, consistent with Padé interpolations between the 3−ε expansion and the exact 2d minimal model.

  6. Bootstrapping 3D Conformal Field Theories with Product Analytic Functionals

    hep-th 2026-08 conditional novelty 6.5 of 10

    A bootstrap method using product analytic functionals gives stronger, faster-converging bounds in three-dimensional conformal field theory, including a new kink near external dimension 4.16.

  7. Bootstrapping the Simplest Deconfined Quantum Critical Point

    hep-th 2025-07 conditional novelty 6.0 of 10

    Conformal bootstrap bounds for U(1)-charged scalars in 3d are saturated by the CP^2 model's large-N and lattice predictions, suggesting the CP^2 deconfined quantum critical point is a conformal field theory.

  8. Probing Line Defect CFT with Mixed-Correlator Bootstrability

    hep-th 2024-12 conditional novelty 6.0 of 10

    Using mixed-correlator bootstrability with parity and localization input, this paper produces new finite-coupling bounds on 12 OPE coefficients and a new exact BPS structure constant for the Maldacena-Wilson line defect CFT.

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