Rigorous Limits on the Interaction Strength in Quantum Field Theory

Abstract

We derive model-independent, universal upper bounds on the Operator Product Expansion (OPE) coefficients in unitary 4-dimensional Conformal Field Theories. The method uses the conformal block decomposition and the crossing symmetry constraint of the 4-point function. In particular, the OPE coefficient of three identical dimension $d$ scalar primaries is found to be bounded by ~ 10(d-1) for 1<d<1.7. This puts strong limits on unparticle self-interaction cross sections at the LHC.

arXiv comment11 pp, 3 figs + data file attached

References in corpus (18)

• Gauge Theory Correlators from Non-Critical String Theory
• Large N Field Theories, String Theory and Gravity
• Electric-Magnetic Duality in Supersymmetric Non-Abelian Gauge Theories
• Bounding scalar operator dimensions in 4D CFT
• Conformal Four Point Functions and the Operator Product Expansion
• Unparticle Physics
• Conformal Partial Waves and the Operator Product Expansion
• Lattice Study of Conformal Behavior in SU(3) Yang-Mills Theories
• Universal Constraints on Conformal Operator Dimensions
• Exact AdS/CFT spectrum: Konishi dimension at any coupling
• Operator Product Expansion of the Lowest Weight CPOs in N=4 SYM_4 at Strong Coupling
• Evidence for a conformal phase in SU(N) gauge theories
• Scale and conformal invariance in field theory: a physical counterexample
• Phase structure of lattice QCD for general number of flavors
• Why Unparticle Models with Mass Gaps are Examples of Hidden Valleys
• Unparticle Self-Interactions and Their Collider Implications
• Unparticle Self-Interactions at the Large Hadron Collider
• Collider Effects of Unparticle Interactions in Multiphoton Signals

Cited by in corpus (78)

• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Solving the 3D Ising Model with the Conformal Bootstrap
• Projectors, Shadows, and Conformal Blocks
• The Bootstrap Program for Boundary CFT_d
• Bootstrapping the O(N) Vector Models
• Spinning Conformal Blocks
• OPE Convergence in Conformal Field Theory
• Bounds on 4D Conformal and Superconformal Field Theories
• Bootstrapping Conformal Field Theories with the Extremal Functional Method
• Radial Coordinates for Conformal Blocks
• The $(2,0)$ superconformal bootstrap
• Effective Conformal Theory and the Flat-Space Limit of AdS
• Bootstrapping the 3d Ising twist defect
• A Mellin space approach to the conformal bootstrap
• Conformal Partial Waves: Further Mathematical Results
• Bounds in 4D Conformal Field Theories with Global Symmetry
• Carving out OPE space and precise $O(2)$ model critical exponents
• Conformal Field Theories in Fractional Dimensions
• Weight Shifting Operators and Conformal Blocks
• The S-matrix Bootstrap II: Two Dimensional Amplitudes
• Central Charge Bounds in 4D Conformal Field Theory
• Bootstrapping phase transitions in QCD and frustrated spin systems
• Five dimensional $O(N)$-symmetric CFTs from conformal bootstrap
• Diagonal Limit for Conformal Blocks in d Dimensions
• Conformal Blocks for Arbitrary Spins in Two Dimensions
• The 3d Stress-Tensor Bootstrap
• Bootstrapping $O(N)$ Vector Models in $4<d<6$
• Bounds on $\mathcal{N}=1$ Superconformal Theories with Global Symmetries
• Spinning Witten Diagrams
• Into the EFThedron and UV constraints from IR consistency
• Approaching conformal window of $O(n)\times O(m)$ symmetric Landau-Ginzburg models from conformal bootstrap
• Eikonalization of Conformal Blocks
• The superconformal bootstrap for structure constants
• $\mathcal{N}=1$ Superconformal Blocks for General Scalar Operators
• PyCFTBoot: A flexible interface for the conformal bootstrap
• Bootstrapping Mixed Correlators in the Five Dimensional Critical O(N) Models
• The S-matrix Bootstrap IV: Multiple Amplitudes
• A Semidefinite Program Solver for the Conformal Bootstrap
• Casimir recursion relations for general conformal blocks
• Remarks on the Convergence Properties of the Conformal Block Expansion
• Non-Abelian Binding Energies from the Lightcone Bootstrap
• Holographic dual of the five-point conformal block
• Bootstrapping Pions at Large $N$
• On critical exponents without Feynman diagrams
• Conformal Bootstrap in Three Dimensions?
• On the four-point function of the stress-energy tensors in a CFT
• Navigator Function for the Conformal Bootstrap
• Bootstrapping the 3d Ising Stress Tensor
• Conformal Bootstrap Approach to O(N) Fixed Points in Five Dimensions
• Holographic OPE Coefficients from AdS Black Holes with Matters
• Spinning Geodesic Witten Diagrams
• Superembedding Methods for Current Superfields
• Inverse Bootstrapping Conformal Field Theories
• The unitary subsector of generalized minimal models
• Charting the space of 3D CFTs with a continuous global symmetry
• New method for the conformal bootstrap with OPE truncations
• Minimal Distances Between SCFTs
• Correlators of Mixed Symmetry Operators in Defect CFTs
• Bootstrap Bounds on Closed Einstein Manifolds
• Bootstrapping Closed Hyperbolic Surfaces
• An Automated Generation of Bootstrap Equations for Numerical Study of Critical Phenomena
• Bounds from LEP on unparticle interactions with electroweak bosons
• Bootstrapping mixed correlators in $\mathcal{N}=4$ Super Yang-Mills
• Bootstrap Bounds on Closed Hyperbolic Manifolds
• Bounds on SCFTs from Conformal Perturbation Theory
• CFT4 as SO(4,2)-invariant TFT2
• Scalar Unparticle Signals at the LHC
• Unitarity violation in non-integer dimensional Gross-Neveu-Yukawa model
• Non-chiral 2d CFT with integer energy levels
• Bootstrapping frustrated magnets: the fate of the chiral $\mathrm{O}(N)\times \mathrm{O}(2)$ universality class
• Bounds on Triangle Anomalies in (3+1)d
• autoboot: A generator of bootstrap equations with global symmetry
• Deconstructing Conformal Blocks in 4D CFT
• The Goldstone Equivalence Theorem and AdS/CFT
• The Operator Product Expansion in Quantum Field Theory
• Global Study of Electron-Quark Unparticle Interactions
• A Note on Bounds of Scalar Operators in Perturbative SCFTs
• Analytic Studies of Fermions in the Conformal Bootstrap