Chronon Field Theory in 1+1 Dimensions: A Solvable Framework for Emergent Geometry, Gauge Fields, and Mass

We present a dimensionally reduced formulation of Chronon Field Theory in 1+1 dimensions that serves as a fully solvable framework for the unified emergence of spacetime geometry, gauge structure, and quantized matter. The theory is based on a single unit-norm timelike vector field whose internal phase simultaneously encodes curvature and U(1) holonomy. We derive exact topological soliton solutions, which manifest as charged, massive excitations, and identify three physically distinct but interrelated manifestations of mass arising from the field’s internal structure: gradient mass (inertial response), holonomy mass (topological sector), and coherence mass (interference-based quantization). A linearized analysis around solitonic backgrounds reveals emergent photon- and graviton-like modes, while composite configurations exhibit discrete mass spectra tied to coherence conditions. The model thus provides an analytically tractable setting for investigating the geometric and topological origin of matter, charge analogues, and mass hierarchy within the broader Chronon framework.