Gauge Enhanced Quantum Criticality Beyond the Standard Model

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.