Derives explicit OPE coefficients for contact and exchange Witten diagrams and closed-form defect-to-bulk crossing kernels for zero- and surface defects in specific dimensions.
The analytic functional bootstrap. Part II. Natural bases for the crossing equation
4 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We clarify the relationships between different approaches to the conformal bootstrap. A central role is played by the so-called extremal functionals. They are linear functionals acting on the crossing equation which are directly responsible for the optimal bounds of the numerical bootstrap. We explain in detail that the extremal functionals probe the Regge limit. We construct two complete sets of extremal functionals for the crossing equation specialized to $z=\bar{z}$, associated to the generalized free boson and fermion theories. These functionals lead to non-perturbative sum rules on the CFT data which automatically incorporate Regge boundedness of physical correlators. The sum rules imply universal properties of the OPE at large $\Delta$ in every unitary solution of SL(2) crossing. In particular, we prove an upper and lower bound on a weighted sum of OPE coefficients present between consecutive generalized free field dimensions. The lower bound implies the $\phi\times\phi$ OPE must contain at least one primary in the interval $[2\Delta_{\phi}+2n,2\Delta_{\phi}+2n+4]$ for all sufficiently large integer $n$. The functionals directly compute the OPE decomposition of crossing-symmetrized Witten exchange diagrams in $AdS_2$. Therefore, they provide a derivation of the Polyakov bootstrap for SL(2), in particular fixing the so-called contact-term ambiguity. We also use the resulting sum rules to bootstrap several Witten diagrams in $AdS_2$ up to two loops.
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hep-th 4years
2026 4roles
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A prototype successfully upgrades low-order extremal flow solutions to high numerical order for gap maximization in a simple spinning modular bootstrap test case.
Simple feed-forward neural networks trained on crossing symmetry plus a single anchor value reproduce CFT correlators to percent-level accuracy, and the authors conjecture this works because physical correlators are the smoothest allowed functions.
Simple neural networks trained on crossing symmetry and one anchor point reproduce conformal correlators to within a few percent across many CFTs.
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Aspects of Witten Diagrams for Holographic Defects
Derives explicit OPE coefficients for contact and exchange Witten diagrams and closed-form defect-to-bulk crossing kernels for zero- and surface defects in specific dimensions.
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Upgrading Extremal Flows in the Space of Derivatives
A prototype successfully upgrades low-order extremal flow solutions to high numerical order for gap maximization in a simple spinning modular bootstrap test case.
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Neural Spectral Bias and Conformal Correlators I: Introduction and Applications
Simple feed-forward neural networks trained on crossing symmetry plus a single anchor value reproduce CFT correlators to percent-level accuracy, and the authors conjecture this works because physical correlators are the smoothest allowed functions.
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Neural Networks Reveal a Universal Bias in Conformal Correlators
Simple neural networks trained on crossing symmetry and one anchor point reproduce conformal correlators to within a few percent across many CFTs.