Scalar modular bootstrap and zeros of the Riemann zeta function
Nathan Benjamin, Cyuan-Han Chang
Abstract
A bstract Using the technology of harmonic analysis, we derive a crossing equation that acts only on the scalar primary operators of any two-dimensional conformal field theory with U(1) c symmetry. From this crossing equation, we derive bounds on the scalar gap of all such theories. Rather remarkably, our crossing equation contains information about all nontrivial zeros of the Riemann zeta function. As a result, we rephrase the Riemann hypothesis purely as a statement about the asymptotic density of scalar operators in certain two-dimensional conformal field theories. We discuss generalizations to theories with only Virasoro symmetry.
Topics & Concepts
PhysicsRiemann hypothesisRiemann zeta functionScalar (mathematics)Mathematical physicsModular designQuantum electrodynamicsPure mathematicsMathematicsGeometryOperating systemComputer scienceAnalytic Number Theory Researchadvanced mathematical theoriesMathematical functions and polynomials