[Paper Review] Gauge Enhanced Quantum Criticality Between Grand Unifications: Categorical Higher Symmetry Retraction

Juven Wang, Yi‐Zhuang You|arXiv (Cornell University)|Nov 19, 2021

Black Holes and Theoretical Physics102 references26 citations

TL;DR

This paper expands the quantum landscape of Grand Unification by refining U(5) gauge groups to U(5)_{\

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) $su(4) imes su(2) imes su(2)$ 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 $(u(1) imes u(1)) times \mathbb{Z}_2$, the fusion rule of 2d topological surface operator splits. However, the un-Higgs Spin(10) at UV retracts this categorical symmetry.

Motivation & Objective

• Motivate the SM as a low-energy vacuum arising near quantum criticality between neighbor GUT-like vacua in a quantum phase diagram.
• Refine the gauge-theory structure of GG and Barr’s flipped models as U(5)_{0}-type groups with specific q embeddings.
• Investigate how higher global/categorical symmetries and their anomalies constrain GUT-like vacua and transitions.
• Demonstrate the existence of 3+1d deconfined quantum criticalities beyond Landau-Ginzburg paradigms in this GUT landscape.
• Explore how gauging discrete flip symmetries leads to non-invertible (categorical) symmetries and their retraction inside Spin(10).

Proposed method

• Define refined U(5)_{0} gauge groups as U(5)_{0} ? with specific identifications of centers, yielding three non-isomorphic types: U(5)_{0} (q=1,4 analogous), U(5)_{0} (q=2,3), and U(5)_{0}  SU(5) imes U(1).
• Embed Spin(10) within these refined groups to compare subgroup structures and lifting properties.
• Use a 4d Wess-Zumino-Witten (WZW) term to match a mod 2 global mixed gauge-gravity anomaly w2 w3 at the quantum critical region between GG SU(5) and PS vacua.
• Characterize the quantum landscape via a mother effective field theory for a modified so(10) GUT and analyze symmetry realizations in global vs gauged forms.
• Demonstrate that GG and flipped u(5) are two vacua of the same order parameter separated by a first-order Landau-Ginzburg transition.
• Investigate 3+1d deconfined quantum criticalities between GG and PS, and between flipped u(5) and PS, as beyond-Landau-Ginzburg phenomena.

Experimental results

Research questions

• RQ1 What refined group structures are required for GG and Barr’s flipped models to realize a consistent U(5) gauge description?
• RQ2 How do higher global/categorical symmetries arise in SM/GUT contexts, and how are they matched or retracted across different vacua?
• RQ3 Can 3+1d deconfined quantum criticalities occur between neighboring GUT-like vacua beyond the Landau-Ginzburg paradigm?
• RQ4 What role does the w2 w3 mod 2 anomaly play in maintaining quantum criticality between GG and PS or flipped u(5) vacua?
• RQ5 How does gauging a Z2 flip symmetry affect potential non-invertible (categorical) symmetries and their fate in Spin(10)?

Key findings

• The precise GG or flipped u(5) gauge group requires a refined Lie group U(5)_{0} with
  6hat{q}=2 or 3, distinct from non-isomorphic
  6hat{q}=1 or 4.
• For 16n Weyl fermions, GG and flipped u(5) are two different symmetry-breaking vacua of the same order parameter separated by a first-order Landau-Ginzburg transition.
• 3+1d deconfined quantum criticalities exist between GG and PS, and between flipped u(5) and PS, which lie beyond the Landau-Ginzburg paradigm.
• Topological quantum criticality can occur by tuning between 15n and 16n Weyl fermion scenarios.
• Gauging the Z2 flip symmetry between GG and flipped u(5) models suggests a potential categorically higher (non-invertible) symmetry, realized by a certain gauge sector, which retracts when embedded into Spin(10).