Latent Geometry and the Emergence of Lorentzian Time in Matrix Quantum Mechanics

Abstract

We introduce \emph{latent geometry} in BFSS/BMN models. Before an emergent geometry evaporates at the geometric transition, large-$d$ Gaussianization encodes its information in the exceptional $N=2$ sector selected by the baby fuzzy sphere, a single active spin-$1/2$ Pauli block. Dimensional reduction, finite-$N$ Gaussianization and exact Molien--Weyl projection transport this encoding to mass-deformed BFSS${}_2$. At $N=2$, the same stable BFSS${}_2$ oscillator admits inequivalent unitary ${\mathbf{H}}_{\theta }^2={\mathbf{EAdS}}_{\theta }^2$ and ${\mathbf{dS}}_{\theta }^2$ decodings, realizing spacetime transmutation and the emergence of Lorentzian time.

Comments: 7 pages, 1 figure, one table