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 GeorgiGlashow (GG) $su(5)$ and PatiSalam (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 WessZumino Witten term matching a 4d nonperturbative global mixed gaugegravity $w_2 w_3$ anomaly. In this work, we include Barr's flipped $su(5)$ model into the quantum landscape, showing these four GUTlike 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 nonisomorphic 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 symmetrybreaking vacua of the same order parameter separated by a firstorder LandauGinzburg 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 LandauGinzburg 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 noninvertible 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 unHiggs Spin(10) at UV retracts this categorical symmetry.
 Publication:

arXiv eprints
 Pub Date:
 November 2021
 DOI:
 10.48550/arXiv.2111.10369
 arXiv:
 arXiv:2111.10369
 Bibcode:
 2021arXiv211110369W
 Keywords:

 High Energy Physics  Theory;
 Condensed Matter  Strongly Correlated Electrons;
 High Energy Physics  Lattice;
 High Energy Physics  Phenomenology;
 Mathematical Physics
 EPrint:
 65 pages. Sequel to arXiv:2106.16248. Dedicate to the anniversaries of Subir Sachdev (60), XiaoGang Wen (60), Edward Witten (70), ShingTung Yau (72). Sec 5 on Generalized Higher Symmetries of Standard Models and Grand Unifications, Sec 6 on Potential Categorical Symmetry. v2: misprints corrected