Energy's and amplitudes' positivity
Dec, 2009
21 pages
Published in:
- JHEP 05 (2010) 095,
- JHEP 11 (2011) 128 (erratum)
e-Print:
- 0912.4258 [hep-th]
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Abstract: (arXiv)
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.Note:
- 21 pages. v2: Typos in eq. (2.41) and (2.41) corrected/ discussion of section 2.3 modified accordingly. Other sections and conclusions unchanged. Matches the Erratum published in JHEP
- Spontaneous Symmetry Breaking
- Classical Theories of Gravity
- Conformal and W Symmetry
- null-energy condition
- stability
- dispersion relation
- S-matrix
- general relativity
- fluctuation
- tensor: energy-momentum
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