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Superluminality and UV completion / G. M Shore; Graham Shore
Nuclear Physics B, Volume: 778, Issue: 3, Pages: 219 - 258
Swansea University Author: Graham, Shore
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DOI (Published version): 10.1016/j.nuclphysb.2007.03.034
The idea that the existence of a consistent UV completion satisfying the fundamental axioms of local quantum field theory or string theory may impose positivity constraints on the couplings of the leading irrelevant operators in a low-energy effective field theory is critically discussed. Violation...
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The idea that the existence of a consistent UV completion satisfying the fundamental axioms of local quantum field theory or string theory may impose positivity constraints on the couplings of the leading irrelevant operators in a low-energy effective field theory is critically discussed. Violation of these constraints implies superluminal propagation, in the sense that the low-frequency limit of the phase velocity vph(0) exceeds c. It is explained why causality is related not to vph(0) but to the high-frequency limit vph(∞) and how these are related by the Kramers-Kronig dispersion relation, depending on the sign of the imaginary part of the refractive index Im n(ω) which is normally assumed positive. Superluminal propagation and its relation to UV completion is investigated in detail in three theories: QED in a background electromagnetic field, where the full dispersion relation for n(ω) is evaluated numerically for the first time and the role of the null energy condition Tμνkμkν ≥ 0 is highlighted; QED in a background gravitational field, where examples of superluminal low-frequency phase velocities arise in violation of the positivity constraints; and light propagation in coupled laser-atom Λ-systems exhibiting Raman gain lines with Im n(ω) < 0. The possibility that a negative Im n(ω) must occur in quantum field theories involving gravity to avoid causality violation, and the implications for the relation of IR effective field theories to their UV completion, are carefully analysed.
This paper demonstrates that the relation between low-energy effective field theories and their UV completion is more subtle than previously believed and shows that in theories involving gravity at least one apparently fundamental tenet of QFT and S-matrix theory must be violated.
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