Energy Flux Positivity and Unitarity in CFTs

Abstract

We show that in most conformal field theories the condition of the energy flux positivity, proposed by Hofman and Maldacena, is equivalent to the absence of ghosts. At finite temperature and large energy and momenta, the two-point functions of the stress energy tensor develop lightlike poles. The residues of the poles can be computed, as long as the only spin two conserved current, which appears in the stress energy tensor OPE and acquires nonvanishing expectation value at finite temperature, is the stress energy tensor. The condition for the residues to stay positive and the theory to remain ghost free is equivalent to the condition of positivity of energy flux.

11 pages, harvmac; v2: some clarifications and a reference added

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• Higher Derivative Gravity, Causality and Positivity of Energy in a UV complete QFT
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• Anisotropic Flows into Black Holes
• Partition functions of higher derivative conformal fields on conformally related spaces
• Freedom near Lightcone and ANEC Saturation
• Holographic RG Flows from Quasi-Topological Gravity