Lining up a Positive Semi-Definite Six-Point Bootstrap

Abstract

In this work we initiate a positive semi-definite numerical bootstrap program for multi-point correlators. Considering six-point functions of operators on a line we reformulate the crossing symmetry equation for a pair of comb-channel expansions as a semi-definite programming problem. We provide two alternative formulations of this problem. At least one of them turns out to be amenable to numerical implementation. Through a combination of analytical and numerical techniques we obtain rigorous bounds on CFT data in the triple-twist channel for several examples.

arXiv comment45 pages + appendices, 13 figures; v2: added references, minor clarifications and details on numerical implementation, matches JHEP version

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Cited by in corpus (5)

• Bootstrapping the 3d Ising Stress Tensor
• Conformal Blocks in Two and Four Dimensions from Oscillator Representations
• Sparsity in the numerical six-point bootstrap
• Wilson Loops with Lagrangians: Large Spin OPE and Cusp Anomalous Dimension Dictionary
• Five-point partial waves, splitting constraints and hidden zeros