Constructing the Infrared Conformal Generators on the Fuzzy Sphere

Abstract

We investigate the conformal algebra on the fuzzy sphere, and in particular the generators of translations and special conformal transformations which are emergent symmetries in the infinite IR but are broken along the RG flow. We show how to extract these generators using the energy momentum tensor, which is complicated by the fact that one does not have a priori access to the energy momentum tensor of the CFT limit but rather must construct it numerically. We discuss and quantitatively analyze the main sources of corrections to the conformal generators due to the breaking of scale-invariance at finite energy, and develop efficient methods for removing these corrections. The resulting generators have matrix elements that match CFT predictions with accuracy varying from sub-percent level for the lowest-lying states up to several percent accuracy for states with dimension $\sim 5$ with $N=16$ fermions. We show that the generators can be used to accurately identify primary operators vs descendant operators in energy ranges where the spectrum is too dense to do the identification solely based on the approximate integer spacing within conformal multiplets.

31 pages, 13 figures; v2: minor corrections, journal version

References in corpus (20)

• Solving the 3D Ising Model with the Conformal Bootstrap
• The Lightcone Bootstrap and the Spectrum of the 3d Ising CFT
• Conformal dimensions via large charge expansion
• On the CFT Operator Spectrum at Large Global Charge
• Uncovering conformal symmetry in the $3D$ Ising transition: State-operator correspondence from a fuzzy sphere regularization
• Heavy Operators and Hydrodynamic Tails
• Landau Level Quantization on the Sphere
• Extraction of conformal data in critical quantum spin chains using the Koo-Saleur formula
• Rigorous bounds on irrelevant operators in the 3d Ising model CFT
• The $\mathrm{SO}(5)$ Deconfined Phase Transition under the Fuzzy Sphere Microscope: Approximate Conformal Symmetry, Pseudo-Criticality, and Operator Spectrum
• Operator Product Expansion Coefficients of the 3D Ising Criticality via Quantum Fuzzy Sphere
• Rotating superfluids and spinning charged operators in conformal field theory
• Studying the 3d Ising surface CFTs on the fuzzy sphere
• Thermalization and chaos in a 1+1d QFT
• 3D Ising CFT and Exact Diagonalization on Icosahedron: The Power of Conformal Perturbation Theory
• Solving Conformal Defects in 3D Conformal Field Theory using Fuzzy Sphere Regularization
• Numerical tests of the large charge expansion
• Quantum Monte Carlo Simulation of the 3D Ising Transition on the Fuzzy Sphere
• Snowmass White Paper: Hamiltonian Truncation
• Ising BCFT from Fuzzy Hemisphere

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• A new series of 3D CFTs with $\mathrm{Sp}(N)$ global symmetry on fuzzy sphere
• Regularizing 3D conformal field theories via anyons on the fuzzy sphere
• Critical Majorana fermion at a topological quantum Hall bilayer transition
• Numerical extraction of crosscap coefficients in microscopic models for (2+1)D conformal field theory
• Conformal Data for the O(3) Wilson-Fisher Conformal Field Theory from Fuzzy Sphere Realization of the Quantum Rotor Model
• Free and Interacting Fermionic Conformal Field Theories on the Fuzzy Sphere
• A Fuzzy Sphere Journey in Critical Phenomena
• The $O(N)$ Free-Scalar and Wilson-Fisher Conformal Field Theories on the Fuzzy Sphere