Abstract
In QFT, the null energy condition (NEC) for a classical field configuration is usually associated with that configuration’s stability against small perturbations, and with the sub-luminality of these. Here, we exhibit an effective field theory that allows for stable NEC-violating solutions with exactly luminal excitations only. The model is the recently introduced ‘galileon’, or more precisely its conformally invariant version. We show that the theory’s low-energy S-matrix obeys standard positivity as implied by dispersion relations. However we also show that if the relevant NEC-violating solution is inside the effective theory, then other (generic) solutions allow for superluminal signal propagation. While the usual association between sub-luminality and positivity is not obeyed by our example, that between NEC and sub-luminality is, albeit in a less direct way than usual.
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ArXiv ePrint: 0912.4258
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Nicolis, A., Rattazzi, R. & Trincherini, E. Energy’s and amplitudes’ positivity. J. High Energ. Phys. 2010, 95 (2010). https://doi.org/10.1007/JHEP05(2010)095
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DOI: https://doi.org/10.1007/JHEP05(2010)095