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

Abstract

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.

16 pages

References in corpus (11)

• Near-horizon symmetries of extremal black holes
• Quantum Entropy Function from AdS(2)/CFT(1) Correspondence
• Near Extremal Black Hole Entropy as Entanglement Entropy via AdS2/CFT1
• Entropy Function and AdS(2)/CFT(1) Correspondence
• Central Charge for AdS_2 Quantum Gravity
• Extremal vacuum black holes in higher dimensions
• Ads(3)/CFT(2) to Ads(2)/CFT(1)
• The H=xp model revisited and the Riemann zeros
• Landau levels and Riemann zeros
• Particle dynamics on AdS_2 x S^2 background with two-form flux
• States of a chiral 2d CFT

Cited by in corpus (10)

• Protected $SL(2,\mathbb{R})$ Symmetry in Quantum Cosmology
• Polymer Quantum Cosmology: Lifting quantization ambiguities using a $SL(2,\mathbb{R})$ conformal symmetry
• Klein four-group and Darboux duality in conformal mechanics
• Implications of Conformal Symmetry in Quantum Mechanics
• Class of solutions of the Wheeler-DeWitt equation in the Friedmann-Robertson-Walker universe
• Spectral Properties of the Symmetry Generators of Conformal Quantum Mechanics: A Path-Integral Approach
• Conformal quantum mechanics and holography in noncommutative space-time
• The AdS^2_θ/CFT_1 Correspondence and Noncommutative Geometry I: A QM/NCG Correspondence
• Conformal mechanical treatment of Calogero-Moser model and infinite dimensional Lie algebra of conformal Galilei type
• The AdS^2_θ/CFT_1 Correspondence and Noncommutative Geometry II: Noncommutative Quantum Black Holes