Analytic and Numerical Bootstrap of CFTs with $O(m)\times O(n)$ Global Symmetry in 3D

Abstract

Motivated by applications to critical phenomena and open theoretical questions, we study conformal field theories with $O(m)\times O(n)$ global symmetry in $d=3$ spacetime dimensions. We use both analytic and numerical bootstrap techniques. Using the analytic bootstrap, we calculate anomalous dimensions and OPE coefficients as power series in $\epsilon =4-d$ and in $1/n$, with a method that generalizes to arbitrary global symmetry. Whenever comparison is possible, our results agree with earlier results obtained with diagrammatic methods in the literature. Using the numerical bootstrap, we obtain a wide variety of operator dimension bounds, and we find several islands (isolated allowed regions) in parameter space for $O(2)\times O(n)$ theories for various values of $n$. Some of these islands can be attributed to fixed points predicted by perturbative methods like the $\epsilon$ and large-$n$ expansions, while others appear to arise due to fixed points that have been claimed to exist in resummations of perturbative beta functions.

arXiv comment43 pages, 15 figures. v2: 44 pages, 15 figures. Comments and references added. v3: 46 pages, 15 figures. Comments, references and a few tables with results added. v4: Corrected typo in (3.47), references added

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• Dispersive CFT Sum Rules
• Selected Topics in Analytic Conformal Bootstrap: A Guided Journey
• The critical O(N) CFT: Methods and conformal data
• Rigorous bounds on irrelevant operators in the 3d Ising model CFT
• New Developments in the Numerical Conformal Bootstrap
• Non-Wilson-Fisher kinks of $O(N)$ numerical bootstrap: from the deconfined phase transition to a putative new family of CFTs
• Bootstrapping Monodromy Defects in the Wess-Zumino Model
• Long-range multi-scalar models at three loops
• Heavy Handed Quest for Fixed Points in Multiple Coupling Scalar Theories in the $\epsilon$ Expansion
• The chiral phase transition and the axial anomaly
• Seeking SUSY fixed points in the $4-\epsilon$ expansion
• Spectrum continuity and level repulsion: the Ising CFT from infinitesimal to finite $\mathbf{\epsilon }$
• Perturbative and Nonperturbative Studies of CFTs with MN Global Symmetry
• CFTs with $U(m)\times U(n)$ Global Symmetry in 3D and the Chiral Phase Transition of QCD
• Anomalous $U(1{)}_A$ couplings and the Columbia plot
• The tri-fundamental quartic model
• Three-dimensional lattice SU($N_c$) gauge theories with multiflavor scalar fields in the adjoint representation
• Bootstrapping Mixed MN Correlators in 3D
• Navigating through the O(N) archipelago
• Analytic bootstrap for magnetic impurities
• The tricritical Ising CFT and conformal bootstrap
• Bootstrapping frustrated magnets: the fate of the chiral $\mathrm{O}(N)\times \mathrm{O}(2)$ universality class
• Anomalous Dimensions in Hypercubic Theories
• Addendum: Long-range multi-scalar models at three loops
• Emergent Supersymmetry at Large $N$
• Fine Spectrum from Crude Analytic Bootstrap
• First-order transition in the stacked-$J_1$-$J_2$ Ising model on a cubic lattice
• Conformal Bootstrap with Duality-Inspired Fusion Rule
• Multi-fixed point numerical conformal bootstrap: a case study with structured global symmetry