2025/07/11 by Marine De Clerck, Sean A. Hartnoll, De Clerck, Marine +2 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Mathematical Theories and Applications #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometry and complex manifolds #High Energy Physics - Theory (hep-th)
paper · pdf · doi:10.48550/arxiv.2507.08788
openalex publication_date 2025/07/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The near-singularity BKL dynamics of five dimensional gravity and supergravity (and also an extended four-dimensional supergravity) is known to be given by the billiard problem of a particle within a fundamental domain of the Bianchi groups PSL(2,\mathcal O) ⊂ PSL(2,ℂ), acting on ℍ3. Here \mathcal O are the Gaussian or Eisenstein integers, which define a square or triangular lattice in ℂ. The Wheeler-DeWitt wavefunctions near the singularity are, correspondingly, automorphic Maass forms of PSL(2,\mathcal O). We show how these wavefunctions are associated to certain L-functions evaluated along their critical axis. Each of these L-functions admits an Euler product representation over the complex primes P\mathcal O ⊂ \mathcal O. From this fact we write the L-function as the trace over an auxiliary Hilbert space of charged harmonic oscillators, labeled by the complex primes P\mathcal O. In this way we have constructed a 'dual' primon gas partition function for the wavefunction of the universe close to a five dimensional cosmological singularity.