Graviton scattering and a sum rule for the c anomaly in 4D CFT

• Published in: The journal of high energy physics 2018-09, Vol.2018 (9), p.1-51, Article 25
• Main Authors: Gillioz, Marc, Lu, Xiaochuan, Luty, Markus A.
• Format: Article
• Language: English
• Subjects: Anomalies in Field and String Theories; Classical and Quantum Gravitation; Coefficients; Conformal Field Theory; Elementary Particles; Existence theorems; High energy physics; Lower bounds; Minkowski space; Momentum; Physics; Physics and Astronomy; PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Scattering; String Theory
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP09(2018)025

A bstract 4D CFTs have a scale anomaly characterized by the coefficient c , which appears as the coefficient of logarithmic terms in momentum space correlation functions of the energy-momentum tensor. By studying the CFT contribution to 4-point graviton scattering amplitudes in Minkowski space we derive a sum rule for c in terms of TT O OPE coefficients. The sum rule can be thought of as a version of the optical theorem, and its validity depends on the existence of the massless and forward limits of the 〈 TTTT 〉 correlation functions that contribute. The finiteness of these limits is checked explicitly for free scalar, fermion, and vector CFTs. The sum rule gives c as a sum of positive terms, and therefore implies a lower bound on c given any lower bound on TT O OPE coefficients. We compute the coefficients to the sum rule for arbitrary operators of spin 0 and 2, including the energy-momentum tensor.