Interacting Topological Insulator and Emergent Grand Unified Theory

Abstract

Motivated by the Pati-Salam Grand Unified Theory, we study $(4+1)d$ topological insulators with $SU(4)\times SU(2{)}_1\times SU(2{)}_2$ symmetry, whose $(3+1)d$ boundary has 16 flavors of left-chiral fermions, which form representations $(4,2,1)$ and $(\bar{4},1,2)$. The key result we obtain is that, without any interaction, this topological insulator has a $\mathbb{Z}$ classification, namely any quadratic fermion mass operator at the $(3+1)d$ boundary is prohibited by the symmetries listed above; while under interaction this system becomes trivial, namely its $(3+1)d$ boundary can be gapped out by a properly designed short range interaction without generating nonzero vacuum expectation value of any fermion bilinear mass, or in other words, its $(3+1)d$ boundary can be driven into a "strongly coupled symmetric gapped (SCSG) phase". Based on this observation, we propose that after coupling the system to a dynamical $SU(4)\times SU(2{)}_1\times SU(2{)}_2$ lattice gauge field, the Pati-Salam GUT can be fully regularized as the boundary states of a $(4+1)d$ topological insulator with a {\it thin} fourth spatial dimension, the thin fourth dimension makes the entire system generically a $(3+1)d$ system. The mirror sector on the opposite boundary will {\it not} interfere with the desired GUT, because the mirror sector is driven to the SCSG phase by a carefully designed interaction and is hence decoupled from the GUT.

arXiv comment8 pages, 3 figures

References in corpus (35)

• Unpaired Majorana fermions in quantum wires
• Topological Field Theory of Time-Reversal Invariant Insulators
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Periodic table for topological insulators and superconductors
• A Method for Simulating Chiral Fermions on the Lattice
• Topological phases of fermions in one dimension
• Topological Defects and Gapless Modes in Insulators and Superconductors
• The effects of interactions on the topological classification of free fermion systems
• Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect
• Infinitely many regulator fields for chiral fermions
• Classification of Topological Insulators and Superconductors
• Symmetry-protected topological orders for interacting fermions -- Fermionic topological nonlinear $\sigma$ models and a special group supercohomology theory
• Interacting fermionic topological insulators/superconductors in three dimensions
• Topological classification with additional symmetries from Clifford algebras
• Emergent Photons and New Transitions in the O(3) Sigma Model with Hedgehog Suppression
• Classifying gauge anomalies through SPT orders and classifying gravitational anomalies through topological orders
• Interacting topological phases and modular invariance
• Symmetry Enforced Non-Abelian Topological Order at the Surface of a Topological Insulator
• A Time-Reversal Invariant Topological Phase at the Surface of a 3D Topological Insulator
• Gapped Symmetry Preserving Surface-State for the Electron Topological Insulator
• Interaction effect on topological classification of superconductors in two dimensions
• The effect of interactions on 2D fermionic symmetry-protected topological phases with Z2 symmetry
• A new class of $(2+1)$-d topological superconductor with ${\mathbb{Z}}_8$ topological classification
• Symmetry protected topological phases in non-interacting fermion systems
• Symmetry Protected Topological States of Interacting Fermions and Bosons
• On the origin of artificial electrodynamics and other stories in three-dimensional bosonic models
• Symmetries, Dimensions, and Topological Insulators: the mechanism behind the face of the Bott clock
• A lattice non-perturbative definition of an SO(10) chiral gauge theory and its induced standard model
• Spacetime as a topological insulator: Mechanism for the origin of the fermion generations
• Investigation of the Domain Wall Fermion Approach to Chiral Gauge Theories on the Lattice
• Chiral Lattice Gauge Theories Via Mirror-Fermion Decoupling: A Mission (im)Possible?
• Domain wall fermions in a waveguide: the phase diagram at large Yukawa coupling
• Stochastic series expansion algorithm for the S=1/2 XY model with four-site ring exchange
• On the decoupling of mirror fermions
• Bosonic Short Range Entangled states Beyond Group Cohomology classification

Cited by in corpus (46)

• Zoo of quantum-topological phases of matter
• Choreographed entangle dances: topological states of quantum matter
• A theory of 2+1D bosonic topological orders
• Symmetric Mass Generation
• Symmetric Fermion Mass Generation as Deconfined Quantum Criticality
• Origin of fermion masses without spontaneous symmetry breaking
• Fermion mass without symmetry breaking
• Symmetry protected topological phases under decoherence
• Bona fide interaction-driven topological phase transition in correlated SPT states
• A Solution to the 1+1D Gauged Chiral Fermion Problem
• A Non-Perturbative Definition of the Standard Models
• Nonperturbative Regulator for Chiral Gauge Theories?
• Fermion masses through four-fermion condensates
• Novel phases in strongly coupled four-fermion theories
• Topological invariants for interacting topological insulators: II. Breakdown of the Green's function formalism
• Fermion masses without symmetry breaking in two spacetime dimensions
• Quantum Monte Carlo study of strange correlator in interacting topological insulators
• Anomalies and symmetric mass generation for Kaehler-Dirac fermions
• Topological Electromagnetic Responses of Bosonic Quantum Hall, Topological Insulator, and Chiral Semi-Metal phases in All Dimensions
• The Origin of Families and $SO(18)$ Grand Unification
• Gauge Enhanced Quantum Criticality Between Grand Unifications: Categorical Higher Symmetry Retraction
• 't Hooft anomalies for staggered fermions
• A Chiral Solution to the Ginsparg-Wilson Equation
• Chiral Lattice Fermions From Staggered Fields
• Ultra Unification
• Anomaly and Cobordism Constraints Beyond the Standard Model: Topological Force
• Unwinding Fermionic SPT Phases: Supersymmetry Extension
• Topology and strong four fermion interactions in four dimensions
• Fermi Surface Symmetric Mass Generation
• Gauge Enhanced Quantum Criticality Beyond the Standard Model
• On the gauge invariant path-integral measure for the overlap Weyl fermions in $\underline{16}$ of SO(10)
• Why is the mission impossible? -- Decoupling the mirror Ginsparg-Wilson fermions in the lattice models for two-dimensional abelian chiral gauge theories
• Long-range Coulomb Interaction effects on Topological Phase Transitions between Semi-metals and Insulators
• Polaron in a $p+ip$ Fermi topological superfluid
• Interacting Topological Insulators with Synthetic Dimensions
• Phases of a strongly coupled four-fermion theory
• Four interactions in the sedenion curved spaces
• Anomaly and Cobordism Constraints Beyond Grand Unification: Energy Hierarchy
• Four revolutions in physics and the second quantum revolution -- a unification of force and matter by quantum information
• Induced topological gravity and anomaly inflow from Kaehler-Dirac fermions in odd dimensions
• CT or P Problem and Symmetric Gapped Fermion Solution
• A no-go result for implementing chiral symmetries by locality-preserving unitaries in a 3 dimensional Hamiltonian lattice model of fermions
• Metallic states beyond Tomonaga-Luttinger liquids in one dimension
• Lattice Regularization of Reduced Kähler-Dirac Fermions and Connections to Chiral Fermions
• Volume and Topological Invariants of Quantum Many-body Systems
• Deconfined Quantum Criticality among Grand Unified Theories