Neural networks optimized solely on crossing symmetry reconstruct CFT correlators from minimal input data to few-percent accuracy across generalized free fields, minimal models, Ising, N=4 SYM, and AdS diagrams.
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Uncovering Conformal Symmetry in the 3D Ising Transition: State-Operator Correspondence from a Quantum Fuzzy Sphere Regularization
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2026 13representative citing papers
Thermal inversion formulas produce asymptotically accurate CFT data for heavy operators that remains reliable at intermediate dimensions and survives first-order bulk interactions.
Adding a cubic two-body interaction to quantum rotors on the fuzzy sphere isolates the cubic CFT critical point, enabling calculation of scaling dimensions for key operators that match existing benchmarks.
OPE-based recursive renormalization for mixed composite operators gives five-loop anomalous dimensions in phi^4 and two-loop in phi^3 models.
Bose-Kondo impurities with spins S=1/2, 1, and 3/2 each flow to distinct stable interacting conformal defects despite sharing the same symmetry and anomaly.
Four PT-symmetric 1+1D quantum models are mapped to the Yang-Lee critical point via state-operator correspondence and bosonization, with scaling dimensions matching exact 2D results and a numerically confirmed growing two-point function.
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.
Proposal for an experimental test of conformal invariance in critical phenomena via grazing-incidence scattering that checks a momentum-space differential constraint on the cross-section.
Hardware-efficient gates are universal for state preparation in particle-number and symmetry-constrained subspaces because commutators generate Pauli Z projectors that span the full so(w) and su(w) algebras.
Numerical extraction of scaling dimensions and OPE coefficients for 32 primary operators in the O(2) Wilson-Fisher CFT via fuzzy-sphere regularization shows agreement with bootstrap predictions.
Neural networks trained on crossing symmetry accurately reconstruct conformal correlators from minimal inputs due to alignment between their spectral bias and CFT smoothness.
Proposes and numerically tests a reconstructed Hamiltonian for approximate CFT ground states in any dimension that recovers CFT spectral properties.
Lecture notes develop semiclassical methods to compute large-n scaling dimensions of composite operators in CFTs, recovering known results in free theory and deriving one-loop corrections at the Wilson-Fisher fixed point.
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