Title: Positive energy conditions in 4D conformal field theory

Abstract

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.

Authors:

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

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+ Show Author Affiliations

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

Publication Date:

Mon Oct 03 00:00:00 EDT 2016

Research Org.:

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

Sponsoring Org.:

USDOE

OSTI Identifier:

1364045

Grant/Contract Number:  

FG02-91ER40674

Resource Type:

Accepted Manuscript

Journal Name:

Journal of High Energy Physics (Online)

Additional Journal Information:

Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2016; Journal Issue: 10; Journal ID: ISSN 1029-8479

Publisher:

Springer Berlin

Country of Publication:

United States

Language:

English

Subject:

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