AdS2/CFT1, Whittaker vector and Wheeler-De Witt equation

Tadashi Okazaki

AdS2/CFT1, Whittaker vector and Wheeler-De Witt equation

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arxiv 1510.04759 v1 pith:EHR5JCEA submitted 2015-10-16 hep-th math.NTquant-ph

Tadashi Okazaki This is my paper · ORCID

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keywords functionconformalmechanicsquantumads2dilatationequationexpectation

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We study the energy representation of conformal quantum mechanics as the Whittaker vector without specifying classical Lagrangian. We show that a generating function of expectation values among two excited states of the dilatation operator in conformal quantum mechanics is a solution to the Wheeler-DeWitt equation and it corresponds to the AdS2 partition function evaluated as the minisuperspace wave function in Liouville field theory. We also show that the dilatation expectation values in conformal quantum mechanics lead to the asymptotic smoothed counting function of the Riemann zeros.

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