Abstract
We apply numerical conformal bootstrap techniques to the four-point function of a Weyl spinor in 4d non-supersymmetric CFTs. We find universal bounds on operator dimensions and OPE coefficients, including bounds on operators in mixed symmetry representations of the Lorentz group, which were inaccessible in previous bootstrap studies. We find discontinuities in some of the bounds on operator dimensions, and we show that they arise due to a generic yet previously unobserved “fake primary” effect, which is related to the existence of poles in conformal blocks. We show that this effect is also responsible for similar discontinuities found in four-fermion bootstrap in 3d, as well as in the mixed-correlator analysis of the 3d Ising CFT. As an important byproduct of our work, we develop a practical technology for numerical approximation of general 4d conformal blocks.
Highlights
Introduction and summary of resultsConsiderable progress has been achieved during the last ten years in the understanding of conformal field theories (CFTs) in d ≥ 3 space-time dimensions
We find universal bounds on operator dimensions and operator product expansion (OPE) coefficients, including bounds on operators in mixed symmetry representations of the Lorentz group, which were inaccessible in previous bootstrap studies
We summarize here the analytic expressions found for the products of the neutral OPE coefficients
Summary
Considerable progress has been achieved during the last ten years in the understanding of conformal field theories (CFTs) in d ≥ 3 space-time dimensions. This was triggered by the pioneering work [1] where it was shown how to efficiently apply the conformal bootstrap program [2, 3] using numerical methods. Using as heuristic guiding principle the idea that discontinuities of this kind are hints of the presence of consistent CFTs, the numerical conformal bootstrap allows to discover new theories and compute their CFT data by using extremal functional methods [9,10,11,12,13,14,15]
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