Gauge and Poincare′ properties of the UV cutoff and UV completion in quantum field theory

The UV cutoff on a quantum field theory (QFT) can explicitly break or conserve the Poincare (translation) symmetry. And the very same cutoff can explicitly break or conserve the gauge symmetry. In the present work, we perform a systematic study of the UV cutoff in regard to its gauge and Poincare properties and construct UV completions restoring the broken gauge symmetry. In the case of the Poincare-conserving UV cutoff, we find that the gauge symmetry gets restored via the Higgs mechanism. In the case of Poincare-breaking UV cutoff, however, we find that the flat spacetime affine curvature takes the place of the Higgs field and, when taken to curved spacetime, gauge symmetry gets restored at the extremum of the metric-affine action. We also find that gravity emerges at the extremum if the QFT under concern consists of new particles beyond the known ones. The resulting emergent gravity plus renormalized QFT setup has the potential to reveal itself in various astrophysical, cosmological, and collider phenomena.

Automated summary

This study systematically investigates the impact of the UV cutoff on gauge and Poincare symmetries, and constructs UV completions that restore the broken gauge symmetry. It is found that the gauge symmetry is restored via the Higgs mechanism under the Poincare-conserving UV cutoff. However, under the Poincare-breaking UV cutoff, the flat spacetime affine curvature replaces the Higgs field, and gauge symmetry is restored at the extremum of the metric-affine action when taken to curved spacetime. It is also discovered that gravity emerges at the extremum if the QFT under consideration includes new particles. The resulting emergent gravity plus renormalized QFT setup has the potential to manifest itself in various astrophysical, cosmological, and collider phenomena.