TY - JOUR

T1 - Momentum space CFT correlators for Hamiltonian truncation

AU - Anand, Nikhil

AU - Khandker, Zuhair U.

AU - Walters, Matthew T.

N1 - 31+9 pages, 2 figures; v2: small typos fixed; v3: minor clarifications added, typo in AdS expression fixed

PY - 2020/10/15

Y1 - 2020/10/15

N2 - 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 2F1 hypergeometric functions, allowing for efficient numerical evaluation. As a concrete application, we work out matrix elements for 3d ϕ4-theory, thus providing the seed ingredients for future truncation studies.

AB - 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 2F1 hypergeometric functions, allowing for efficient numerical evaluation. As a concrete application, we work out matrix elements for 3d ϕ4-theory, thus providing the seed ingredients for future truncation studies.

KW - hep-th

U2 - 10.1007/JHEP10(2020)095

DO - 10.1007/JHEP10(2020)095

M3 - Article

SN - 1126-6708

VL - 2020

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

M1 - 95

ER -