Gauge Enhanced Quantum Criticality Beyond the Standard Model (2106.16248v3)

Abstract: Standard lore views our 4d quantum vacuum governed by one of the candidate Standard Models (SMs), while lifting towards some Grand Unification-like structure (GUT) at higher energy scales. In contrast, in our work, we introduce an alternative view that the SM arises from various neighbor vacua competition in a quantum phase diagram. In general, we regard the SM arising near the gapless quantum criticality (either critical points or critical regions) between the competing neighbor vacua. In particular, we demonstrate how the $su(3)\times su(2)\times u(1)$ SM with 16n Weyl fermions arises near the quantum criticality between the GUT competition of Georgi-Glashow (GG) $su(5)$ and Pati-Salam (PS) $su(4)\times su(2)\times su(2)$. We propose two enveloping toy models. Model I is a conventional $so(10)$ GUT with a Spin(10) gauge group plus GUT-Higgs potential inducing various Higgs transitions. Model II modifies Model I plus a 4d discrete torsion Wess-Zumino-Witten-like term built from GUT-Higgs field (that matches a nonperturbative global mixed gauge-gravity anomaly captured by a 5d invertible topological field theory $w_2w_3$), which manifests a Beyond-Landau-Ginzburg criticality between GG and PS models, with extra Beyond-the-Standard-Model (BSM) excitations emerging near a quantum critical region. If the internal symmetries were treated as global symmetries, we show a gapless 4d deconfined quantum criticality with new BSM fractionalized fragmentary excitations of Color-Flavor separation, and gauge enhancement including a Dark Gauge force sector, altogether requiring a double fermionic Spin structure named DSpin. If the internal symmetries are dynamically gauged, we show a 4d boundary criticality such that only appropriately gauge enhanced dynamical GUT gauge fields propagate into an extra-dimensional 5d bulk. The phenomena may be regarded as SM deformation or morphogenesis.

• The paper introduces a novel view on the Standard Model emerging from quantum criticality in competing grand unified vacua.
• It develops two models—one without and one with a WZW term—to capture nonperturbative anomaly dynamics and topological effects.
• It suggests new experimental avenues by predicting deconfined quantum critical behavior and emergent excitations beyond traditional gauge theories.

An Exploration of Gauge Enhanced Quantum Criticality Beyond the Standard Model

The paper "Gauge Enhanced Quantum Criticality Beyond the Standard Model" by Juven Wang and Yi-Zhuang You introduces a novel perspective on the structure and origins of the Standard Model (SM) within the framework of competing quantum vacua. This work proposes that the SM is not merely the low-energy effective field theory we experience in our universe but an emergent phase arising near quantum critical points between various grand unified theories (GUTs). Such a view departs from the traditional approach of simply seeking higher unifying theories at elevated energy scales, which has been the prevailing paradigm in particle physics.

Key Insights and Theoretical Framework

The core theoretical innovation presented in this paper involves examining the SM as situated within a larger landscape of possible vacuum states, with particular focus on quantum criticality induced by competition between these vacua. Specifically, the authors illustrate how the well-known SM gauge group $SU(3) \times SU(2) \times U(1)$ can appear near the quantum critical region between configurations of Georgi-Glashow $SU(5)$ and Pati-Salam $SU(4) \times SU(2) \times SU(2)$ models, nested within an overarching $SO(10)$ GUT.

Two primary model-building approaches are introduced:

1. Model I considers the $SO(10)$ GUT without an additional Wess-Zumino-Witten (WZW) term, aiming to explore traditional transition mechanisms without the constraints of nonperturbative anomalies.
2. Model II applies a modification through the introduction of a 4-dimensional WZW-like term designed to encode nontrivial topological interactions between GUT-Higgs fields. This framework introduces new anomaly-induced phenomena beyond simple gauge symmetry breaking.

Quantum Criticality and Beyond Standard Model Excitations

The paper suggests that quantum critical regions, especially those exhibiting deconfined quantum criticality, can lead to emergent excitation modes distinct from traditional Landau-Ginzburg-Wilson critical points. In their "Fragmentary GUT-Higgs Liquid" model, fields become fractionalized near the critical regime into new excitations—fermionic partons and emergent gauge fields—and are fundamentally influenced by the anisotropic topology of these quantum phases.

Notably, the notion of deconfined quantum criticality in four dimensions represents a significant departure from well-trodden paths in three-dimensional condensed matter systems. Through careful construction, the $w_2w_3$ anomaly is not just an abstract mathematical construct but emerges as a tangible constraint shaping the behavior and interactions of SM constituents and potential heavy dark matter candidates.

Implications for Theoretical and Practical Extensions

The authors' framework points to several critical implications. Practically, it opens new experimental avenues for probing the boundaries of the Standard Model by tuning parameters in such a way as to access neighboring GUT phases at achievable energy scales, potentially even within currently feasible experiments. Theoretically, it challenges the hierarchy and boundary definitions between phases in the quantum field theory landscape, ultimately suggesting that phase competition at quantum critical points may represent a natural order and unified underlying framework for particle physics.

Furthermore, the proposed models and mechanisms inject additional components into the theoretical menagerie of particle physics, offering explanations for heavy and light dark matter candidates through their emerging dynamics, and call for a re-evaluation of how fermion masses and anomalies interplay within gauge theories.

Future Directions

While the framework is robustly defined, the exact path to unification of these ideas with experimental quantum chromodynamics and the search for underlying topological features in cosmological data remains outstanding. This research beckons further paper into how the unconventional features of gauge-enhanced quantum criticality can manifest in observable physics, and whether these insights can more robustly predict phenomena such as proton decay or more exotic particle states.

This perspective centrally posits that changing how we look at phase diagrams in high energy physics—from vertical energy scales to broader, richer multidimensional landscapes of varying vacua—can lead to transformative insights into the foundational forces governing our universe. As the field moves towards considering interplays between space, symmetry, and topology, such reimaginings of phase structure and transitions could redefine our approach to cosmology and quantum field theory.