Ultra Unification

TL;DR

This paper proposes a new theoretical framework extending the Standard Model and GUT by incorporating gapped Topological Phase Sectors and Topological Force, which involve advanced topological quantum field theories and could revolutionize high-energy physics.

Contribution

It introduces a novel unification approach beyond GUT by integrating topological phases, anomaly cancellation, and extended objects, expanding the conceptual landscape of fundamental interactions.

Findings

Introduction of gapped Topological Phase Sectors consistent with anomaly constraints

Proposal of a new Topological Force mediated by extended topological objects

Potential implications for high-energy physics beyond conventional particle theories

Abstract

Strong, electromagnetic, and weak forces were unified in the Standard Model (SM) with spontaneous gauge symmetry breaking. These forces were further conjectured to be unified in a simple Lie group gauge interaction in the Grand Unification (GUT). In this work, we propose a theory beyond the SM and GUT by adding new gapped Topological Phase Sectors consistent with the nonperturbative global anomaly cancellation and cobordism constraints (especially from the baryon minus lepton number ${\bf B}-{\bf L}$, the electroweak hypercharge $Y$, and the mixed gauge-gravitational anomaly). Gapped Topological Phase Sectors are constructed via symmetry extension, whose low energy contains unitary Lorentz invariant topological quantum field theories (TQFTs): either 3+1d non-invertible TQFT, or 4+1d invertible or non-invertible TQFT (short-range or long-range entangled gapped phase). Alternatively, there could also be right-handed "sterile" neutrinos, gapless unparticle physics, more general interacting conformal field theories, or gravity with topological cobordism constraints, or their combinations to altogether cancel the mixed gauge-gravitational anomaly. We propose that a new high-energy physics frontier beyond the conventional 0d particle physics relies on the new Topological Force and Topological Matter including gapped extended objects (gapped 1d line and 2d surface operators or defects, etc., whose open ends carry deconfined fractionalized particle or anyonic string excitations) or gapless conformal matter. Physical characterizations of these gapped extended objects require the mathematical theories of cohomology, cobordism, or category. Although weaker than the weak force, Topological Force is infinite-range or long-range which does not decay in the distance, and mediates between the linked worldvolume trajectories via fractional or categorical statistical interactions.