A new series of 3D CFTs with $\mathrm{Sp}(N)$ global symmetry on fuzzy sphere

Abstract

The quest to discover new 3D CFTs has been intriguing for physicists. For this purpose, fuzzy sphere reguarlisation that studies interacting quantum systems defined on the lowest Landau level on a sphere has emerged as a powerful tool. In this paper, we discover a series of new CFTs with global symmetry $\mathrm{Sp}(N)$ in the fuzzy sphere models that are closely related to the $\mathrm{SO}(5)$ deconfined phase transition, and are described by a $\mathrm{Sp}(N)/(\mathrm{Sp}(M)\times \mathrm{Sp}(N-M))$ non-linear sigma model with a Wess-Zumino-Witten term. We numerically verify the emergent conformal symmetry by observing the integer-spaced conformal multiplets and studying the finite-size scaling of the conformality. We discuss possible candidates for these newly discovered CFTs, the most plausible ones being Chern-Simons-matter theories which have $N$ flavour of gapless bosons or fermions coupled to a non-Abelian (viz. $\mathrm{Sp}(1)$, $\mathrm{Sp}(2)$, etc.) Chern-Simons gauge field. Our work provides new avenues for studying interacting CFTs in 3D, possibly facilitating the non-perturbative study of critical gauge theories and previously undiscovered CFTs.

arXiv comment13+17 pages, 4+4 figures, 1+5 tables

References in corpus (43)

• "Deconfined" quantum critical points
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Spontaneous Inter-layer Coherence in Double-Layer Quantum-Hall Systems I: Charged Vortices and Kosterlitz-Thouless Phase Transitions
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Deconfined quantum critical points: symmetries and dualities
• Emergent Photons and New Transitions in the O(3) Sigma Model with Hedgehog Suppression
• Quantum criticality with two length scales
• Walking, Weak first-order transitions, and Complex CFTs
• Particle-Vortex Duality from 3d Bosonization
• Scaling in the Fan of an Unconventional Quantum Critical Point
• Antiferromagnetic to valence-bond-soild transitions in two-dimensional SU(N) Heisenberg models with multi-spin interactions
• Emergent $SO(5)$ Symmetry at the Néel to Valence-Bond-Solid Transition
• Deconfined Quantum Criticality, Scaling Violations, and Classical Loop Models
• Comments on Global Symmetries, Anomalies, and Duality in (2+1)d
• Chern-Simons-matter dualities with $SO$ and $USp$ gauge groups
• Mott Transition in An Anyon Gas
• Walking, Weak first-order transitions, and Complex CFTs II. Two-dimensional Potts model at $Q>4$
• Deconfined criticality flow in the Heisenberg model with ring-exchange interactions
• Néel to valence-bond solid transition on the honeycomb lattice: Evidence for deconfined criticality
• A Symmetry Breaking Scenario for QCD${}_3$
• A continuous transition between fractional quantum Hall and superfluid states
• Uncovering conformal symmetry in the $3D$ Ising transition: State-operator correspondence from a fuzzy sphere regularization
• Phases of the (2+1) dimensional SO(5) non-linear sigma model with topological term
• Stiefel Liquids: Possible Non-Lagrangian Quantum Criticality from Intertwined Orders
• Half-filled Landau levels: a continuum and sign-free regularization for 3D quantum critical points
• The $\mathrm{SO}(5)$ Deconfined Phase Transition under the Fuzzy Sphere Microscope: Approximate Conformal Symmetry, Pseudo-Criticality, and Operator Spectrum
• Phase transitions out of quantum Hall states in moiré materials
• Operator Product Expansion Coefficients of the 3D Ising Criticality via Quantum Fuzzy Sphere
• Holography for $\mathcal{N}=1^{\ast }$ on $S^4$
• New Developments in the Numerical Conformal Bootstrap
• Emergent Multi-flavor QED3 at the Plateau Transition between Fractional Chern Insulators: Applications to graphene heterostructures
• Wess-Zumino-Witten Terms in Graphene Landau Levels
• Field-induced QCD${}_3$-Chern-Simons quantum criticalities in Kitaev materials
• The $g$-function and Defect Changing Operators from Wavefunction Overlap on a Fuzzy Sphere
• Studying the 3d Ising surface CFTs on the fuzzy sphere
• Phases of (2+1)D SO(5) non-linear sigma model with a topological term on a sphere: multicritical point and disorder phase
• 3D Ising CFT and Exact Diagonalization on Icosahedron: The Power of Conformal Perturbation Theory
• Critical behavior in the cubic dimer model at nonzero monomer density
• Quantum Hall Transition near a Fermion Feshbach Resonance in a Rotating Trap
• Constructing the Infrared Conformal Generators on the Fuzzy Sphere
• Quantum Monte Carlo Simulation of the 3D Ising Transition on the Fuzzy Sphere

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