The Shortest Scale of Quantum Field Theory

TL;DR

The paper proposes an N-dependent ultraviolet cutoff in quantum field theories to ensure gravitational stability of the Minkowski vacuum, with implications for entropy bounds and holography.

Contribution

It introduces a new N-dependent ultraviolet cutoff scale in quantum field theories coupled to gravity, addressing vacuum stability issues.

Findings

Ultraviolet cutoff scales as M_Planck/N^{1/4}.

Bound is consistent with entropy bounds and holography.

Relaxed but does not eliminate the N bound from entropy considerations.

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 $M_Planck/N^1/4$. 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.