Work

Whittaker vector, Wheeler-DeWitt equation, and the gravity dual of conformal quantum mechanics

Year: 2015

Type: article

Abstract: We study the energy representation of conformal quantum mechanics as the Whittaker vector without specifying the 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 ${\mathrm{AdS}}_{2}$ 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.

Source: Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

DOI: 10.1103/physrevd.92.126010

Author: Tadashi Okazaki

Institution: National Taiwan University

Language: English

Topic: Black Holes and Theoretical Physics

Subfield: Nuclear and High Energy Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funder: Ministry of Science and Technology of the People's Republic of China

Award: G8762238211