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Prior work [arXiv:2106.16248] shows that the Standard Model (SM) naturallyarises 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 quantumvacua (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 discreteWess-Zumino Witten term matching a 4d nonperturbative global mixedgauge-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 modelsarise near the quantum criticality near SM. Highlights include: First, we findthe precise GG or flipped $u(5)$ gauge group requires to redefine a Lie groupU(5)$_{\hat q}$ with $\hat q=2$ or $3$ (instead of non-isomorphic analog $\hatq=1$ or 4), and different $\hat q$ are related by multiple covering. Second, weshow that the GG and flipped $u(5)$ are two different symmetry-breaking vacuaof the same order parameter separated by a first-order Landau-Ginzburgtransition. We also show that analogous 3+1d deconfined quantum criticalities,both between GG and PS, and between the flipped $u(5)$ and PS, are beyondLandau-Ginzburg paradigm. Third, topological quantum criticality occurs bytuning between the 15n vs 16n scenarios. Fourth, we explore the generalizedhigher global symmetries in the SM and GUTs. Gauging the $\mathbb{Z}_2$ flipsymmetry between GG and flipped $u(5)$ models, leads to a potential categoricalhigher 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 topologicalsurface operator splits. However, the un-Higgs Spin(10) at UV retracts thiscategorical symmetry.

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