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Skydiving to Bootstrap Islands

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arxiv 2307.13046 v1 pith:BP7LQWRU submitted 2023-07-24 hep-th math.OC

Aike Liu , David Simmons-Duffin , Ning Su , Balt C. van Rees This is my paper · ORCID
classification hep-thmath.OC
keywords bootstrapparameterskydivingspaceexternalfamiliesfindingmoving
verification ladder T0 review T1 audit T2 compute T3 formal

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We study families of semidefinite programs (SDPs) that depend nonlinearly on a small number of "external" parameters. Such families appear universally in numerical bootstrap computations. The traditional method for finding an optimal point in parameter space works by first solving an SDP with fixed external parameters, then moving to a new point in parameter space and repeating the process. Instead, we unify solving the SDP and moving in parameter space in a single algorithm that we call "skydiving". We test skydiving on some representative problems in the conformal bootstrap, finding significant speedups compared to traditional methods.

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Cited by 6 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. 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.

  3. Splitting Regions and Shrinking Islands from Higher Point Constraints

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    Imposing 5-point split conditions and unitarity bounds selects the string beta function as the unique 4-point amplitude, up to equal-mass infinite spin towers.

  4. 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.

  5. 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.

  6. 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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