BKL singularity dynamics are mapped to conformal quantum mechanics whose states are odd automorphic L-functions, and these L-functions are reinterpreted as partition functions of prime-labeled oscillator gases.
AdS2/CFT1, Whittaker vector and Wheeler-De Witt equation
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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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The Conformal Primon Gas at the End of Time
BKL singularity dynamics are mapped to conformal quantum mechanics whose states are odd automorphic L-functions, and these L-functions are reinterpreted as partition functions of prime-labeled oscillator gases.