The causal bootstrap computes rigorous bounds on smeared spectral functions from non-perturbative Euclidean data by optimizing over the convex set of compatible positive spectral densities and reducing dual problems to semidefinite programs for certain kernels.
Scaling the semidefinite program solver SDPB,
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The boundary of the scalar S-matrix island divides into phases with universal high-energy asymptotics and resonance content, each corresponding to a different UV completion mechanism for gapped scalars.
Non-minimal three-point interactions induce negative one-loop running of Wilson coefficients in gravitational EFTs, yet graviton loops generate positive IR contributions that dominate the bounds after smearing if the species number is bounded.
Conformal bootstrap with a sparseness condition produces a cone whose apex matches QMC and fuzzy sphere data for the DQCP, supporting multicriticality via a relevant SO(5) singlet scalar.
A prototype successfully upgrades low-order extremal flow solutions to high numerical order for gap maximization in a simple spinning modular bootstrap test case.
Imposing a duality-inspired fusion rule that forbids the [ε] sector from appearing in the [ε] × [ε] OPE yields numerical bounds on (Δ_σ, Δ_ε) that include the 2d Ising model but exclude the 3d Ising model.