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.
A $p$-adic version of AdS/CFT
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abstract
In this summary of my talk at Strings 2016, I explain how classical dynamics on an infinite tree graph can be dual to a conformal field theory defined over the $p$-adic numbers. An informal introduction to $p$-adic numbers is followed by a presentation of results on holographic three- and four-point functions. The simplicity of $p$-adic field theories and their similarity to ordinary field theories are illustrated through comparisons of holographic correlators and computations of simple loop diagrams on the field theory side. I close with a discussion of challenges and directions for future work.
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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.