Why 4D? Spontaneous Dimensional Selection from Gauge Criticality
arXiv:2607.28615
The paper proposes that the critical behavior of the Yang–Mills coupling at four dimensions can spontaneously select a macroscopic 4D spacetime, demonstrated via a racetrack model with radion stabilization driven by gauge‑criticality‑induced supersymmetry breaking and supergravity effects.
Abstract
Noting that the Yang--Mills coupling is relevant below four dimensions, marginal in four dimensions, and irrelevant above four dimensions, I propose that this criticality can lead to the selection of four macroscopic dimensions. As a proof of principle, I present a concrete racetrack model of the type commonly studied in extra-dimensional scenarios, but without assuming a noncompact 4D spacetime. I find, within a well-controlled model without specifying the 4D, that 4D spacetime is spontaneously realized through radion stabilization via gauge-criticality-induced supersymmetry breaking and supergravity effects.
7pages 3figures