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

Understand

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.