A Toroidal Toy Model for a Finite Universe with Infinite Dynamics: Kaluza-Klein Afotons and Standard Holography

We present a toroidal toy model in which the universe is spatially finite but dynamically infinite. The bulk is five-dimensional anti-de Sitter space, AdS5, with a toroidal boundary T4. Geodesics wrapping the torus never close if the periods are incommensurable, realizing infinite dynamics in a finite space. We identify the afoton as a Kaluza–Klein mode of a bulk scalar, odd under a Z2 symmetry of the torus, and therefore decoupled from the photon. We compute the renormalized action, the Kaluza–Klein spectrum, and the one-loop corrections. The model is technically simpler than its non-orientable companion (forthcoming)), and is compatible with standard holography. As in the companion paper, we emphasize that this is a toy model, not a theory of the observed universe