Conformal Bootstrap Dashing Hopes of Emergent Symmetry

Abstract

We use the conformal bootstrap program to derive necessary conditions for emergent symmetry enhancement from discrete symmetry (e.g. ${\mathbb{Z}}_n$) to continuous symmetry (e.g. $U(1)$) under the renormalization group flow. In three dimensions, in order for ${\mathbb{Z}}_2$ symmetry to be enhanced to $U(1)$ symmetry, the conformal bootstrap program predicts that the scaling dimension of the order parameter field at the infrared conformal fixed point must satisfy ${\Delta }_1>1.08$. We also obtain the similar conditions for ${\mathbb{Z}}_3$ symmetry with ${\Delta }_1>0.580$ and ${\mathbb{Z}}_4$ symmetry with ${\Delta }_1>0.504$ from the simultaneous conformal bootstrap analysis of multiple four-point functions. Our necessary conditions impose severe constraints on many controversial physics such as the chiral phase transition in QCD, the deconfinement criticality in Néel-VBS transitions and anisotropic deformations in critical $O(n)$ models. In some cases, we find that the conformal bootstrap program dashes hopes of emergent symmetry enhancement proposed in the literature.

4+5 pages, v2: improved bound, reference added, appendix added

References in corpus (14)

• "Deconfined" quantum critical points
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• Properties of an algebraic spin liquid on the kagome lattice
• Bootstrapping Mixed Correlators in the 3D Ising Model
• Algebraic spin liquid as the mother of many competing orders
• The critical exponents of the superfluid transition in He4
• Bounds in 4D Conformal Field Theories with Global Symmetry
• From an Antiferromagnet to a Valence Bond Solid: Evidence for a First Order Phase Transition
• Bootstrapping phase transitions in QCD and frustrated spin systems
• Approaching conformal window of $O(n)\times O(m)$ symmetric Landau-Ginzburg models from conformal bootstrap
• Monopoles in CP(N-1) model via the state-operator correspondence
• Transitions to valence-bond solid order in a honeycomb lattice antiferromagnet
• A square lattice algebraic spin liquid with SO(5) symmetry

Cited by in corpus (75)

• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Precision Islands in the Ising and $O(N)$ Models
• Deconfined quantum critical points: symmetries and dualities
• Walking, Weak first-order transitions, and Complex CFTs
• Carving out OPE space and precise $O(2)$ model critical exponents
• Compensating strong coupling with large charge
• Evidence of effective axial U(1) symmetry restoration at high temperature QCD
• A theory of deconfined pseudo-criticality
• Superconductivity from the Condensation of Topological Defects in a Quantum Spin-Hall Insulator
• Note on Wess-Zumino-Witten models and quasiuniversality in 2+1 dimensions
• Abelian Higgs model at four loops, fixed-point collision and deconfined criticality
• Signatures of a Deconfined Phase Transition on the Shastry-Sutherland Lattice: Applications to Quantum Critical SrCu${}_2$(BO${}_3$)${}_2$
• Berry Phase in Quantum Field Theory: Diabolical Points and Boundary Phenomena
• Bootstrapping the long-range Ising model in three dimensions
• Emergence and spontaneous breaking of approximate O(4) symmetry at a weakly first-order deconfined phase transition
• Stiefel Liquids: Possible Non-Lagrangian Quantum Criticality from Intertwined Orders
• Truncatable bootstrap equations in algebraic form and critical surface exponents
• Multicritical deconfined quantum-criticality and Lifshitz point of a helical valence-bond phase
• Scaling of disorder operator at deconfined quantum criticality
• Half-filled Landau levels: a continuum and sign-free regularization for 3D quantum critical points
• The analytic structure of conformal blocks and the generalized Wilson-Fisher fixed points
• Emergent SO(5) symmetry at the columnar ordering transition in the classical cubic dimer model
• Study of the axial U(1) anomaly at high temperature with lattice chiral fermions
• Critical behavior of the QED${}_3$-Gross-Neveu model: Duality and deconfined criticality
• The $\mathrm{SO}(5)$ Deconfined Phase Transition under the Fuzzy Sphere Microscope: Approximate Conformal Symmetry, Pseudo-Criticality, and Operator Spectrum
• Scalar CFTs and Their Large N Limits
• Consistent scaling exponents at the deconfined quantum-critical point
• New Developments in the Numerical Conformal Bootstrap
• Recursion relation for general 3d blocks
• Fermion-induced quantum critical points in three-dimensional Weyl semimetals
• Searching for gauge theories with the conformal bootstrap
• Scaling the semidefinite program solver SDPB
• Easy-plane QED${}_3$'s in the large $N_f$ limit
• Bootstrap bound for conformal multi-flavor QCD on lattice
• Bootstrap experiments on higher dimensional CFTs
• Valence-bond solids, vestigial order, and emergent SO(5) symmetry in a two-dimensional quantum magnet
• Non-Wilson-Fisher kinks of $O(N)$ numerical bootstrap: from the deconfined phase transition to a putative new family of CFTs
• Dirac fermions with plaquette interactions. I. SU(2) phase diagram with Gross-Neveu and deconfined quantum criticalities
• Phases of (2+1)D SO(5) non-linear sigma model with a topological term on a sphere: multicritical point and disorder phase
• Upper bound on the mass anomalous dimension in many-flavor gauge theories: a conformal bootstrap approach
• Conformal bootstrap bounds for the $U(1)$ Dirac spin liquid and $N=7$ Stiefel liquid
• Building models of topological quantum criticality from pivot Hamiltonians
• Emergent O(4) symmetry at the phase transition from plaquette-singlet to antiferromagnetic order in quasi-two-dimensional quantum magnets
• The chiral phase transition and the axial anomaly
• Extracting subleading corrections in entanglement entropy at quantum phase transitions
• Diagnosing $SO(5)$ Symmetry and First-Order Transition in the $J-Q_3$ Model via Entanglement Entropy
• Diagnosing weakly first-order phase transitions by coupling to order parameters
• Evolution of entanglement entropy at SU($N$) deconfined quantum critical points
• Unconventional U(1) to ${\mathbf{Z}}_{\mathbf{q}}$ cross-over in quantum and classical $\mathbf{q}$-state clock models
• Bootstrapping traceless symmetric $O(N)$ scalars
• Valence-Bond Order in a Honeycomb Antiferromagnet Coupled to Quantum Phonons
• Exploring $SU(N)$ adjoint correlators in $3d$
• Anomalous $U(1{)}_A$ couplings and the Columbia plot
• Emergent Symmetry in Quantum Phase Transitions: From Deconfined Quantum Critical Point to Gapless Quantum Spin Liquid
• Anomalous dimensions of spinning operators from conformal symmetry
• Conformal Bootstrap Signatures of the Tricritical Ising Universality Class
• Bootstrapping Mixed MN Correlators in 3D
• An Automated Generation of Bootstrap Equations for Numerical Study of Critical Phenomena
• Conformality and self-duality of $N_f=2$ QED${}_3$
• Emergent self-duality in long range critical spin chain: from deconfined criticality to first order transition
• Can axial U(1) anomaly disappear at high temperature?
• Equilibration of Topological Defects Near the Deconfined Quantum Multicritical Point
• Conformal Fields from Neural Networks
• Axial U(1) symmetry, topology, and Dirac spectra at high temperature in $N_f=2$ lattice QCD
• Deconfined quantum critical point lost in pressurized SrCu2(BO3)2
• QED's in $2+1$ dimensions: complex fixed points and dualities
• Dirac spin liquid as an "unnecessary" quantum critical point on square lattice antiferromagnets
• autoboot: A generator of bootstrap equations with global symmetry
• Exclusion Inside or at the Border of Conformal Bootstrap Continent
• Nematic Antiferromagnetism and Deconfined Criticality from the Interplay between Electron-Phonon and Electron-Electron Interactions
• Deconfined Quantum Critical Point with Non-locality
• Symmetry of screening masses of mesons in two-flavor lattice QCD at high temperatures
• Phase transitions on the dark side of the Gross-Neveu model: Spontaneous $\text{O}(4N)$ symmetry breaking at repulsive coupling
• Deconfined Quantum Phase Transition of a Higher-Order Symmetry-Protected Topological State
• Deconfined pseudocriticality in a model spin-1 quantum antiferromagnet