Coupled minimal models revisited II: Constraints from permutation symmetry

Abstract

Coupling $N$ large $m$ minimal models and flowing to IR fixed points is a systematic way to build new classes of compact unitary 2d CFTs which are likely to be irrational, and potentially have a positive Virasoro twist gap above the vaccuum. In this paper, we build on the construction of [1], establishing that, for spins less than 10, additional currents transforming in non-trivial irreducible representations of the permutation symmetry $S_N$ are not conserved at the IR fixed points. Along the way, we develop a finer understanding of the spectrum of these theories, of the special properties of the $N=4$ case and of non-invertible symmetries that constrain them. We also discuss variations of the original setup of [1] some of which can exist for smaller values of the UV central charge.

35 pages + references, 3 figures, 13 tables; v2: added references, fixed typo, v3: more discussion and code, v4: clarifications, v5: published version

References in corpus (75)

• Generalized Global Symmetries
• Structure Constants and Conformal Bootstrap in Liouville Field Theory
• Two and three-point functions in Liouville theory
• Topological Defect Lines and Renormalization Group Flows in Two Dimensions
• Elliptic Genera of Symmetric Products and Second Quantized Strings
• The Lightcone Bootstrap and the Spectrum of the 3d Ising CFT
• The Worldsheet Dual of the Symmetric Product CFT
• Deriving the ${\text{AdS}}_3/{\text{CFT}}_2$ Correspondence
• Walking, Weak first-order transitions, and Complex CFTs II. Two-dimensional Potts model at $Q>4$
• A scaling theory for the long-range to short-range crossover and an infrared duality
• Long-range critical exponents near the short-range crossover
• Quantum Regge Trajectories and the Virasoro Analytic Bootstrap
• Lightcone Modular Bootstrap and Pure Gravity
• Anomalies and Bounds on Charged Operators
• Renormalisation group calculation of correlation functions for the 2D random bond Ising and Potts models
• Universal Dynamics of Heavy Operators in CFT${}_2$
• On the Higher-Spin Spectrum in Large N Chern-Simons Vector Models
• Anomalous dimensions in CFT with weakly broken higher spin symmetry
• Irrational Conformal Field Theory
• Seeking Fixed Points in Multiple Coupling Scalar Theories in the $\epsilon$ Expansion
• Modular Invariance, Tauberian Theorems, and Microcanonical Entropy
• Light Cone Bootstrap in General 2D CFTs and Entanglement from Light Cone Singularity
• Notes on Spinning Operators in Fermionic CFT
• Words to describe a black hole
• Deligne Categories in Lattice Models and Quantum Field Theory, or Making Sense of $O(N)$ Symmetry with Non-integer $N$
• General Properties of Multiscalar RG Flows in $d=4-\epsilon$
• (2,2) Superconformal Bootstrap in Two Dimensions
• Effect of Random Impurities on Fluctuation-Driven First Order Transitions
• Leading CFT constraints on multi-critical models in d>2
• Coupled Potts models: Self-duality and fixed point structure
• $\epsilon$-Expansion in the Gross-Neveu Model from Conformal Field Theory
• Classical equation of motion and Anomalous dimensions at leading order
• Revisiting the dilatation operator of the Wilson-Fisher fixed point
• Bootstrapping boundary-localized interactions II: Minimal models at the boundary
• Deforming Symmetric Product Orbifolds: A tale of moduli and higher spin currents
• Integrability of Coupled Conformal Field Theories
• Line of fixed points in a bosonic tensor model
• Leading Order Anomalous Dimensions at the Wilson-Fisher Fixed Point from CFT
• $\epsilon$-Expansion in the Gross-Neveu CFT
• Lifting 1/4-BPS States in $Ad{S}_3\times S^3\times T^4$
• Spin--spin critical point correlation functions for the 2D random bond Ising and Potts models
• Coupled minimal models revisited
• Analytic Bootstrap in 2D Boundary Conformal Field Theory: Towards Braneworld Holography
• Global symmetry and conformal bootstrap in the two-dimensional $O(n)$ model
• $\mathcal{N}=2$ Minimal Models: A Holographic Needle in a Symmetric Orbifold Haystack
• Twist accumulation in conformal field theory. A rigorous approach to the lightcone bootstrap
• Thermalization and chaos in a 1+1d QFT
• Heavy Handed Quest for Fixed Points in Multiple Coupling Scalar Theories in the $\epsilon$ Expansion
• The unitary subsector of generalized minimal models
• Scale and Conformal Invariance in Higher Derivative Shift Symmetric Theories
• Leading order CFT analysis of multi-scalar theories in d>2
• On critical models with $N\le 4$ scalars in $d=4-\epsilon$
• The Stranger Things of Symmetric Product Orbifold CFTs
• Spectrum of anomalous dimensions in hypercubic theories
• Spaces of states of the two-dimensional O(n) and Potts models
• Twist Gap and Global Symmetry in Two Dimensions
• Thermal order in large N conformal gauge theories
• Bounds on multiscalar CFTs in the epsilon expansion
• On 2d CFTs that interpolate between minimal models
• Multi-critical multi-field models: a CFT approach to the leading order
• Non-Invertible Symmetry in Calabi-Yau Conformal Field Theories
• Crossing Symmetry in Matter Chern-Simons Theories at finite $N$ and $k$
• Symmetry and universality of multi-field interactions in $6-\epsilon$ dimensions
• The non-rational limit of D-series minimal models
• Critical loop models are exactly solvable
• Lightcone Modular Bootstrap and Tauberian Theory: A Cardy-like Formula for Near-extremal Black Holes
• Slightly broken higher-spin current in bosonic and fermionic QED in the large-$N$ limit
• Models WD_{n} in the presence of disorder and the coupled models
• Anomalous dimensions of partially-conserved higher-spin currents from conformal field theory: bosonic ${\varphi }^{2n}$ theories
• Representation Theory of Solitons
• On Rational Points in CFT Moduli Spaces
• Universal Dynamics in Non-Orientable CFT${}_2$
• Classifying irreducible fixed points of five scalar fields in perturbation theory
• Randomly coupled minimal models
• Anomalous dimensions from conformal field theory: Generalized ${\varphi }^{2n+1}$ theories

Cited by in corpus (4)

• Demystifying integrable QFTs in AdS: No-go theorems for higher-spin charges
• Minimal Models RG flows: non-invertible symmetries & non-perturbative description
• On the Wilson-Fisher fixed point in the limit of integer spacetime dimensions
• Boundary anomalous dimensions from BCFT: O($N$)-symmetric ${\varphi }^{2n}$ theories with a boundary and higher-derivative generalizations