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 $(u(1)\times u(1))⋊{\mathbb{Z}}_2$, the fusion rule of 2d topological surface operator splits. However, the un-Higgs Spin(10) at UV retracts this categorical symmetry.

Comments: 65 pages. Sequel to arXiv:2106.16248. Dedicate to the anniversaries of Subir Sachdev (60), Xiao-Gang Wen (60), Edward Witten (70), Shing-Tung Yau (72). Sec 5 on Generalized Higher Symmetries of Standard Models and Grand Unifications, Sec 6 on Potential Categorical Symmetry. v2: misprints corrected