Gauge and Poincaré 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 Poincaré (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 Poincaré properties and construct UV completions restoring the broken gauge symmetry. In the case of the Poincaré-conserving UV cutoff, we find that the gauge symmetry gets restored via the Higgs mechanism. In the case of Poincaré-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.