Positive energy conditions in 4D conformal field theory

Journal Article · Mon Oct 03 00:00:00 EDT 2016 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/JHEP10(2016)001· OSTI ID:1364045

Farnsworth, Kara ^[1]; Luty, Markus A. ^[1]; Prilepina, Valentina ^[1]

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1. Univ. of California, Davis, CA (United States)

Here, we argue that all consistent 4D quantum field theories obey a spacetime-averaged weak energy inequality < T⁰⁰ > ≥ –C/L⁴, 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.

• Research Organization: Univ. of California, Davis, CA (United States)
• Sponsoring Organization: USDOE
• Grant/Contract Number: FG02-91ER40674
• OSTI ID: 1364045
• Journal Information: Journal of High Energy Physics (Online), Vol. 2016, Issue 10; ISSN 1029-8479
• Publisher: Springer Berlin
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
conformal and W symmetry
effective field theories
space-time symmetries