Ultra Unification (2012.15860v3)

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.

• The paper presents a framework extending grand unified theories by integrating topological phase sectors to cancel persistent gauge-gravitational anomalies.
• It employs symmetry extension methods to construct gapped TQFTs, enabling unitary Lorentz invariant interactions in both 3+1 and 4+1 dimensions.
• The proposal suggests novel implications, including potential dark matter contributions and new long-range interactions that challenge traditional particle models.

An Expert Analysis of Ultra Unification

In this essay, we explore the proposal of Ultra Unification as outlined in Juven Wang's comprehensive paper on Lie group gauge theories and topological phase sectors. This work builds upon the foundation of the Standard Model (SM) and Grand Unified Theories (GUTs), incorporating new dimensions of topological quantum field theories (TQFTs) to address lingering anomalies and limitations inherent in traditional models.

Technical Significance and Results

The paper presents a framework for extending beyond the Standard Model and SU(5) grand unification by integrating concepts from topological phases. It seeks to address nonperturbative global anomalies, particularly the mixed gauge-gravitational anomaly associated with discrete symmetries like baryon minus lepton number $(\mathbf{B - L})$ and electroweak hypercharge $Y$. Notably, the work explores the integration of elements such as right-handed sterile neutrinos and extended topological defects, suggesting these could provide the required anomaly cancellations or reveal new physical phenomena.

A key component of Wang's proposal is the introduction of gapped topological phase sectors. These are constructed via symmetry extension methods, enabling the existence of unitary Lorentz invariant TQFTs at low energies, either as 3+1-dimensional non-invertible TQFTs or 4+1-dimensional invertible or non-invertible TQFTs. These phases offer a novel perspective beyond the traditional zero-dimensional particle view, adding a layer of extended topological objects into the high-energy physics landscape.

Implications and Theoretical Impact

The implications of the Ultra Unification framework are several-fold:

• Anomaly Resolution: By leveraging cobordism constraints and topological sectors, the approach provides a mechanism to cancel anomalies that are otherwise persistent in conventional GUT models. The paper outlines multiple scenarios for anomaly matching, including the addition of new neutrino types or topological field theories.
• Potential for Novel Interactions: The introduction of topological forces, weaker than the weak force but long-range, proposes a new interaction paradigm that might link to unexplored sectors of physics or novel matter states.
• Dark Matter and Neutrinos: The suggestion that the heavy excitations in the gapped phase might contribute to dark matter provides a compelling narrative combining cosmology and particle physics. Similarly, the interaction between neutrinos and these topological phases might offer new insights into neutrino oscillations and mass generation.

Speculation and Future Directions

The proposal that such a framework could account for currently unresolved phenomena in particle physics and cosmology is intriguing. For example, exploring the link between these topological phases and the properties or origins of dark matter could open new experimental avenues. Additionally, future work could investigate specific predictions made by the framework and its compatibility with existing and forthcoming experimental data.

Phase Transitions and Criticality: The notion of topological quantum phase transitions, wherein changes could occur between different effective field theories within the proposed framework, merits further exploration. Such transitions might be key to understanding how discrete topological phases interact with continuous field theories and might hold insights into phenomena such as inflationary cosmology or quantum gravity.

Overall, Wang's Ultra Unification presents a thorough theoretical model combining solid mathematical formalism with imaginative physical insights. The proposal points towards a future where theoretical physics embraces a broader spectrum of topological and geometric influences, potentially leading to new emergent phenomena in the universe's fundamental architectures.