On the four-point function of the stress-energy tensors in a CFT

Abstract

We discuss to what extent the full set of Ward Identities constrain the four-point function of the stress-energy tensors or conserved currents in a conformal field theory. We calculate the number of kinematically unrestricted functional degrees of freedom governing the corresponding correlators and find that it matches the number of functional degrees of freedom governing scattering amplitudes of some "dual" massless particles in the auxiliary Minkowski space. We also formulate the conformal bootstrap constraints for the correlators in question in terms of only unrestricted degrees of freedom. As a by-product we find interesting parallels between solving Ward Identities in coordinate and momentum space.

31 pages, 1 figure

References in corpus (7)

• Conformal collider physics: Energy and charge correlations
• Bootstrapping the O(N) Vector Models
• Bounds on 4D Conformal and Superconformal Field Theories
• The $(2,0)$ superconformal bootstrap
• Bounds in 4D Conformal Field Theories with Global Symmetry
• Central Charge Bounds in 4D Conformal Field Theory
• The superconformal bootstrap for structure constants

Cited by in corpus (32)

• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Spinning AdS Propagators
• The $(2,0)$ superconformal bootstrap
• Operator bases, $S$-matrices, and their partition functions
• The $\mathcal{N}=2$ superconformal bootstrap
• Bootstrapping phase transitions in QCD and frustrated spin systems
• The 3d Stress-Tensor Bootstrap
• Stress-tensor OPE in N=2 Superconformal Theories
• Entanglement entropy across a deformed sphere
• Conformal Collider Physics from the Lightcone Bootstrap
• Color/Kinematics Duality in AdS${}_4$
• Radial expansion for spinning conformal blocks
• Four-point correlation function of stress-energy tensors in N=4 superconformal theories
• PyCFTBoot: A flexible interface for the conformal bootstrap
• Conformal correlators as simplex integrals in momentum space
• A Semidefinite Program Solver for the Conformal Bootstrap
• Spinning operators and defects in conformal field theory
• Casimir recursion relations for general conformal blocks
• Scalar-Vector Bootstrap
• On Conformal Field Theories With Extremal a/c Values
• Bootstrapping the 3d Ising Stress Tensor
• From correlation functions to event shapes in QCD
• Charting the space of 3D CFTs with a continuous global symmetry
• Graviton Scattering and a Sum Rule for the c Anomaly in 4D CFT
• blocks_3d: Software for general 3d conformal blocks
• Bounds on photon scattering
• The Epsilon-Expansion from Conformal Field Theory
• The four-point correlation function of the energy-momentum tensor in the free conformal field theory of a scalar field
• Counting Conformal Correlators
• General Bootstrap Equations in 4D CFTs
• Deconstructing Conformal Blocks in 4D CFT
• Post AdS/CFT