Gauge Enhanced Quantum Criticality Between Grand Unifications: Categorical Higher Symmetry Retraction

Abstract: Prior work [arXiv:2106.16248] shows that the Standard Model (SM) naturally arises near a gapless quantum critical region between Georgi-Glashow (GG) $su(5)$ and Pati-Salam (PS) $su(4) \times su(2) \times su(2)$ models of quantum vacua (in a phase diagram or moduli space), by implementing a modified $so(10)$ Grand Unification (GUT) with a Spin(10) gauge group plus a new discrete Wess-Zumino Witten term matching a 4d nonperturbative global mixed gauge-gravity $w_2 w_3$ anomaly. In this work, we include Barr's flipped $su(5)$ model into the quantum landscape, showing these four GUT-like models arise near the quantum criticality near SM. Highlights include: First, we find the precise GG or flipped $u(5)$ gauge group requires to redefine a Lie group U(5)$_{\hat q}$ with $\hat q=2$ or $3$ (instead of non-isomorphic analog $\hat q=1$ or 4), and different $\hat q$ are related by multiple covering. Second, we show that the GG and flipped $u(5)$ are two different symmetry-breaking vacua of the same order parameter separated by a first-order Landau-Ginzburg transition. We also show that analogous 3+1d deconfined quantum criticalities, both between GG and PS, and between the flipped $u(5)$ and PS, are beyond Landau-Ginzburg paradigm. Third, topological quantum criticality occurs by tuning between the 15n vs 16n scenarios. Fourth, we explore the generalized higher global symmetries in the SM and GUTs. Gauging the $\mathbb{Z}_2$ flip symmetry between GG and flipped $u(5)$ models, leads to a potential categorical higher symmetry that is a non-invertible global symmetry: within a gauge sector $(u(1) \times u(1)) \rtimes \mathbb{Z}_2$, the fusion rule of 2d topological surface operator splits. However, the un-Higgs Spin(10) at UV retracts this categorical symmetry.

• The paper develops a comprehensive quantum phase diagram linking various GUTs through a modified SO(10) model that captures intricate symmetry-breaking patterns.
• It demonstrates how a discrete WZW term drives deconfined quantum criticality and mediates anomalies between models like SU(5) and Pati-Salam.
• The study integrates gauge theoretical insights and fermion representation constraints to reframe categorical higher symmetries in grand unification theories.

An Analysis of Gauge Enhanced Quantum Criticality and Grand Unifications

The academic paper titled "Gauge Enhanced Quantum Criticality Between Grand Unifications: Categorical Higher Symmetry Retraction" by Juven Wang and Yi-Zhuang You explores the intricate relationships between several Grand Unified Theories (GUTs), focusing on the Standard Model (SM), the Georgi-Glashow (GG) SU(5), the flipped SU(5), the Pati-Salam model, and the left-right symmetric models. The crux of this research explores the quantum phase transitions and criticalities stemming from these GUTs, particularly when embedded in a modified $SO(10)$ framework equipped with a discrete Wess-Zumino-Witten (WZW) term.

Key Contributions and Findings

1. Quantum Phase Diagram: The study constructs a comprehensive quantum phase diagram that incorporates various GUTs as distinct phases. By employing a modified $SO(10)$ GUT as the parent effective field theory, the researchers map out how different quantum phases and transitions arise from varying symmetry-breaking patterns, driven by the dynamics of the Higgs fields represented in different dimensional representations.
2. Topological and Quantum Criticalities: Essential to the study is the role of a WZW term added to the $SO(10)$ model, which is vital in capturing a nonperturbative global mixed gauge-gravitational $w_2 w_3$ anomaly. This anomaly mediates the quantum criticality between the GG SU(5) and Pati-Salam models, reflecting a case of deconfined quantum criticality that defies traditional Landau-Ginzburg paradigms.
3. Higher Symmetries and Categorical Structures: The paper examines how the gauged and global symmetries of the SM and GUTs can be understood via their higher symmetries, specifically focusing on 1-form and categorical symmetries. Significantly, the research scrutinizes the potential non-invertible symmetry (categorical symmetry), particularly in the context of swapping two U(5) models using a $_2^{\rm flip}$ symmetry.
4. Gauge Theoretical Considerations: The investigation into the structure of U(5), refined as $(5)_{\hat q}$, and how it integrates into larger symmetries like Spin(10), provides a nuanced understanding of the theoretical frameworks that support gauge criticalities. The researchers effectively demonstrate how the union of such groups inherently results in Spin(10), leading to the retraction of potential categorical symmetries.
5. Implications of Fermion Representations: The consistent integration and distinctions between models that support both 15 and 16 Weyl fermions per generation emphasize constraints imposed by SM phenomenology. The additional exploration of critical regions where $(1)'_{\rm gauge^{\rm dark}}$ becomes deconfined is presented as a distinctive feature of the emergent GUT landscape.

Implications and Future Outlook

This research enriches our understanding of the interplay between different GUTs and their descendants by emphasizing the complexity and richness of their critical phenomena. Practically, the paper’s insights into symmetry classifications and topological orders stand to influence both the theoretical physics community working on unification theories and those concerned with quantum field theory anomalies.

The work suggests several future directions. Developing a deeper understanding of the interaction between categorical symmetries and anomalies in the context of quantum gravity could have significant ramifications for string theory and quantum cosmology. Additionally, further exploration of the mechanism of topological phase transitions between different generations of Weyl fermions may yield novel perspectives on particle physics beyond the Standard Model.

In conclusion, through a rigorous examination of quantum phases and symmetries, this paper offers a critical analysis of GUT models and quantum criticality, paving the way for new investigations into the foundational structure of our universe.