The Shortest Scale of Quantum Field Theory

Abstract

It is suggested that the Minkowski vacuum of quantum field theories of a large number of fields N would be gravitationally unstable due to strong vacuum energy fluctuations unless an N dependent sub-Planckian ultraviolet momentum cutoff is introduced. We estimate this implied cutoff using an effective quantum theory of massless fields that couple to semi-classical gravity and find it (assuming that the cosmological constant vanishes) to be bounded by $M_{P}lanck/N^1/4$. Our bound can be made consistent with entropy bounds and holography, but does not seem to be equivalent to either, and it relaxes but does not eliminate the implied bound on N inherent in entropy bounds.

8 pages. One author added, additional clarifcations and discussions. Figure removed. Version published in PRD

References in corpus (5)

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• The Holographic Principle for General Backgrounds
• Vacuum Energy Density Fluctuations in Minkowski and Casimir States via Smeared Quantum Fields and Point Separation
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