Gauge Enhanced Quantum Criticality Between Grand Unifications: Categorical Higher Symmetry Retraction
Juven Wang, Yi-Zhuang You
TL;DR
This work reframes gauge unification as a quantum-critical problem in a landscape of neighbor GUT vacua, where the SM sits near a gapless region between models like Georgi-Glashow SU(5) and Pati-Salam; it extends this landscape by incorporating Barr's flipped SU(5) and a refined ${\rm U}(5)_{\hat{q}}$ structure that embeds into ${\rm Spin}(10)$. Central to the construction is a modified ${\rm so}(10)$ GUT with a 4d WZW term that matches the mod 2 anomaly $w_2 w_3$, enabling SM-like critical behavior at the boundary between vacua and allowing deconfined quantum criticality in 3+1d regimes. The paper reveals first-order Landau-Ginzburg transitions between GG and flipped vacua, and beyond-Landau-Ginzburg deconfined criticalities near the quantum critical region, while exploring generalized higher symmetries and a potential non-invertible (categorical) symmetry from a ${\mathbb Z}_2^{\rm flip}$ operation that is ultimately retracted upon embedding into Spin(10). Overall, the results propose a coherent framework in which SM phenomenology emerges from a symmetry- and anomaly-protected phase diagram, with implications for generation counting, mass mechanisms, and the role of topological terms in high-energy unification.
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.