Positive energy conditions in 4D conformal field theory

• Published in: The journal of high energy physics 2016-10, Vol.2016 (10), p.1-29, Article 1
• Main Authors: Farnsworth, Kara, Luty, Markus A., Prilepina, Valentina
• Format: Article
• Language: English
• Subjects: ATOMIC AND MOLECULAR PHYSICS; Classical and Quantum Gravitation; conformal and W symmetry; Constants; effective field theories; Elementary Particles; Equivalence; Field theory; High energy physics; Inequalities; Instability; Mathematical analysis; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; space-time symmetries; Stability; String Theory; Tensors
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP10(2016)001

A bstract We argue that all consistent 4D quantum field theories obey a spacetime-averaged weak energy inequality 〈 T 00 〉 ≥ − C/L 4 , where L is the size of the smearing region, and C is a positive constant that depends on the theory. If this condition is violated, the theory has states that are indistinguishable from states of negative total energy by any local measurement, and we expect instabilities or other inconsistencies. We apply this condition to 4D conformal field theories, and find that it places constraints on the OPE coefficients of the theory. The constraints we find are weaker than the “conformal collider” constraints of Hofman and Maldacena. In 3D CFTs, the only constraint we find is equivalent to the positivity of 2-point function of the energy-momentum tensor, which follows from unitarity. Our calculations are performed using momentum-space Wightman functions, which are remarkably simple functions of momenta, and may be of interest in their own right.