Ultra Unification

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 sectors consistent with the nonperturbative global anomaly matching and cobordism constraints (especially from the baryon minus lepton number B − L and the mixed gauge-gravitational anomaly). Gapped topological sectors are constructed via symmetry extension, whose low energy contains unitary topological quantum field theories (TQFTs): either 3+1d non-invertible TQFT (long-range entangled gapped phase), or 4+1d invertible or non-invertible TQFT (short-range or long-range entangled gapped phase), or right-handed neutrinos, or their combinations. 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 anyonic particle or string excitations). 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.

Gauge Enhanced Quantum Criticality Beyond the Standard Model

“…In contrast, Ref. [29][30][31] considers the SM or GUT with 15n Weyl fermions and with a discrete variant of baryon minus lepton number B − L symmetry preserved. Ref.…”

“…Ref. [29][30][31] then suggests the consequences that the missing 16th Weyl fermions can be substituted by additional 4d or 5d gapped topological quantum field theories (TQFTs), or by 4d gapless interacting conformal field theories (CFTs) to saturate a certain Z16 global anomaly. On the other hand, our present work does not introduce these Z16-class anomalous sectors, because we already have implemented the 16n Weyl fermion models that already make the Z16 global anomaly fully cancelled.…”

Cobordism and Deformation Class of the Standard Model

“…[23][24][25][26][27][28][29] consider highly relevant systematic anomaly classifications include several SM-like or Grand Unification (GUT)-like groups. To determine the 4d 't Hooft anomaly and hence the iTFT Z 5 , we gather the cobordism group data from [26,[28][29][30][31][32] to obtain…”

“…For SM with a Z 4,X chiral symmetry, given the fermion content (4), all Z 5 classes of local anomalies in (6) cancel to zero. All extra Z 2 and Z 4 classes of global anomalies in (6) also cancel, but the Z 16 mixed gauge-gravity global anomaly can be nonzero [30,32], whose corresponding 5d iTFT is…”

“…7. Ultra Unification (UU) [30][31][32] replaces some of "right-handed sterile neutrinos" (sterile only to G SMq gauge force, but not sterile to GUT or X forces) by new exotic gapped/gapless sectors (e.g., topological or conformal field theory) or by gravitational sectors with topological origins, via nonperturbative global anomaly cancellation and cobordism constraints. Namely (−3 + n νe,R + n νµ,R + n ντ,R + .…”