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.
Bootstrapping non-unitary CFTs
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abstract
We introduce a non-unitary-compatible numerical bootstrap strategy based on the statistical stability of OPE data inferred from crossing at multiple cross-ratios. For a trial spectrum, crossing determines OPE coefficients whose residual cross-ratio dependence directly measures the truncation error. This defines a scalar objective on the space of spectra, allowing bootstrap searches without imposing unitarity. Applied to two-dimensional Virasoro blocks, the method reproduces known A-series minimal models, including non-unitary examples, and yields candidate truncated solutions for c>1 with crossing violation comparable to that of minimal models. More generally, our framework provides a practical route to solving bootstrap constraints beyond the convex, unitary setting.
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Analytic continuation of marginal couplings produces complex CFTs, with no genuinely complex rational CFTs existing, and exact defect results verified in non-Hermitian Ising and fermion chains.
Machine-learning optimization produces candidate truncated modular-invariant partition functions for 2d CFTs in the central-charge window 1 to 8/7, indicating a continuous solution space and a stricter spectral-gap bound than the prior c/6 + 1/3 limit.
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Neural Spectral Bias and Conformal Correlators I: Introduction and Applications
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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Complex Conformal Manifolds
Analytic continuation of marginal couplings produces complex CFTs, with no genuinely complex rational CFTs existing, and exact defect results verified in non-Hermitian Ising and fermion chains.
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Descending into the Modular Bootstrap
Machine-learning optimization produces candidate truncated modular-invariant partition functions for 2d CFTs in the central-charge window 1 to 8/7, indicating a continuous solution space and a stricter spectral-gap bound than the prior c/6 + 1/3 limit.