Instability of complex CFTs with operators in the principal series

Abstract

We prove the instability of $d$-dimensional conformal field theories (CFTs) having in the operator-product expansion of two fundamental fields a primary operator of scaling dimension $h=d/2+ir$, with non-vanishing $r\in \mathbb{R}$. From an AdS/CFT point of view, this corresponds to a well-known tachyonic instability, associated to a violation of the Breitenlohner-Freedman bound in AdS${}_{d+1}$; we derive it here directly for generic $d$-dimensional CFTs that can be obtained as limits of multiscalar quantum field theories, by applying the harmonic analysis for the Euclidean conformal group to perturbations of the conformal solution in the two-particle irreducible (2PI) effective action. Some explicit examples are discussed, such as melonic tensor models and the biscalar fishnet model.

arXiv comment39 pages, 7 figures. v2: corrected a few typos; v3: added some references, matches published version

References in corpus (65)

• Gauge Theory Correlators from Non-Critical String Theory
• Comments on the Sachdev-Ye-Kitaev model
• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Conformal Partial Waves and the Operator Product Expansion
• The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual
• Analyticity in Spin in Conformal Theories
• Introduction to Nonequilibrium Quantum Field Theory
• Projectors, Shadows, and Conformal Blocks
• Uncolored Random Tensors, Melon Diagrams, and the SYK Models
• Conformal Regge theory
• Conformality Lost
• Walking, Weak first-order transitions, and Complex CFTs
• A universal result on central charges in the presence of double-trace deformations
• Unitarity and the Holographic S-Matrix
• Bi-Local Holography in the SYK Model
• More on Supersymmetric and 2d Analogs of the SYK Model
• New integrable non-gauge 4D QFTs from strongly deformed planar N=4 SYM
• A spacetime derivation of the Lorentzian OPE inversion formula
• Bootstrapping 3D Fermions
• $d$-dimensional SYK, AdS Loops, and $6j$ Symbols
• 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
• Unitarity violation at the Wilson-Fisher fixed point in 4-epsilon dimensions
• $O(N)$ Random Tensor Models
• Bosonic Tensor Models at Large $N$ and Small $\epsilon$
• Perturbative Search for Fixed Lines in Large N Gauge Theories
• Harmonic Analysis and Mean Field Theory
• Spectra of Operators in Large $N$ Tensor Models
• Large N Field Theory and AdS Tachyons
• Strongly γ-deformed N=4 SYM as an integrable CFT
• Crossing Symmetry in Alpha Space
• Integrability of Conformal Fishnet Theory
• Perturbative Gauge Theory and Closed String Tachyons
• Bi-scalar integrable CFT at any dimension
• Spinning Mellin Bootstrap: Conformal Partial Waves, Crossing Kernels and Applications
• A line of CFTs: from generalized free fields to SYK
• AdS Maps and Diagrams of Bi-local Holography
• Prismatic Large $N$ Models for Bosonic Tensors
• A Derivation of AdS/CFT for Vector Models
• 2PI effective action for the SYK model and tensor field theories
• Exact Correlation Functions in Conformal Fishnet Theory
• Anomalous Dimensions from Crossing Kernels
• Generalized Fishnets and Exact Four-Point Correlators in Chiral CFT${}_4$
• Integrable Fishnet from $\gamma$-Deformed $\mathcal{N}=2$ Quivers
• A Complex Fermionic Tensor Model in $d$ Dimensions
• Thermodynamic Bethe Ansatz for Fishnet CFT
• Conformality Loss, Walking, and 4D Complex Conformal Field Theories at Weak Coupling
• Fixed points and the spontaneous breaking of scale invariance
• Line of fixed points in a bosonic tensor model
• Supersymmetric Tensor Model at Large $N$ and Small $\epsilon$
• Spontaneous Breaking of $U(1)$ Symmetry in Coupled Complex SYK Models
• Holographic Complex Conformal Field Theories
• Signs of the time: Melonic theories over diverse number systems
• On the Light dilaton in the Large N Tri-critical O(N) Model
• On Melonic Supertensor Models
• RG Limit Cycles and Unconventional Fixed Points in Perturbative QFT
• The finite $N$ origin of the Bardeen-Moshe-Bander phenomenon and its extension at $N=\infty$ by singular fixed points
• Quantum Spectral Curve of $\gamma$-twisted $\mathcal{N}=4$ SYM theory and fishnet CFT
• Spontaneous Conformal Symmetry Breaking in Fishnet CFT
• Higher melonic theories
• Melonic Dominance in Subchromatic Sextic Tensor Models
• The tri-fundamental quartic model
• Conformal Symmetry and Composite Operators in the $O(N{)}^3$ Tensor Field Theory
• $SO(3)$-invariant phase of the $O(N{)}^3$ tensor model
• The Inversion Formula and 6j Symbol for 3d Fermions

Cited by in corpus (6)

• Non-Perturbative Defects in Tensor Models from Melonic Trees
• Reclaiming the Lost Conformality in a non-Hermitian Quantum 5-state Potts Model
• The F-theorem in the melonic limit
• Phase transitions in tensorial group field theories: Landau-Ginzburg analysis of models with both local and non-local degrees of freedom
• Hidden Critical Points in the Two-Dimensional $O(n>2)$ model: Exact Numerical Study of a Complex Conformal Field Theory
• Coupling renormalization flow in the strongly interacting regime of an asymptotically free quantum field theory in four dimensions