Momentum space CFT correlators for Hamiltonian truncation

Abstract

We consider Lorentzian CFT Wightman functions in momentum space. In particular, we derive a set of reference formulas for computing two- and three-point functions, restricting our attention to three-point functions where the middle operator (corresponding to a Hamiltonian density) carries zero spatial momentum, but otherwise allowing operators to have arbitrary spin. A direct application of our formulas is the computation of Hamiltonian matrix elements within the framework of conformal truncation, a recently proposed method for numerically studying strongly-coupled QFTs in real time and infinite volume. Our momentum space formulas take the form of finite sums over ${}_2{F}_1$ hypergeometric functions, allowing for efficient numerical evaluation. As a concrete application, we work out matrix elements for 3d ${\varphi }^4$-theory, thus providing the seed ingredients for future truncation studies.

arXiv comment31+9 pages, 2 figures; v2: small typos fixed; v3: minor clarifications added, typo in AdS expression fixed

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• Quantum simulation of quantum field theories as quantum chemistry
• Momentum space parity-odd CFT 3-point functions
• On spinning loop amplitudes in Anti-de Sitter space
• A handbook of holographic 4-point functions
• Hamiltonian Truncation Effective Theory
• Effective Hamiltonians and Counterterms for Hamiltonian Truncation
• All plus four point (A)dS graviton function using generalized on-shell recursion relation
• Form Factors and Spectral Densities from Lightcone Conformal Truncation
• ANEC in $\lambda {\varphi }^4$ theory
• Spinors and conformal correlators