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Scalar Modular Bootstrap and Zeros of the Riemann Zeta Function

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BLHW01 - Number theory, machine learning and quantum black holes

We derive a crossing equation that acts only on the scalar primary operators of any 2d CFT . Rather remarkably, our crossing equation contains information about all nontrivial zeros of the Riemann zeta function. As a result, we rephrase the Riemann hypothesis as a statement about the asymptotic density of scalar operators in 2d CFTs. Using this “scalar crossing equation” and cleverly chosen linear functionals, we derive bounds on the scalar gap for these theories. 

This talk is part of the Isaac Newton Institute Seminar Series series.

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