Hadrons on the worldline, holography, and Wilson flow

Holographic principles have impacted the way we look at strong coupling phenomena in quantum chromodynamics, strongly interacting extensions of the standard model, and condensed-matter physics. In real world settings, however, we still lack understanding of why and when such an approach is justified. Therefore, here, without invoking any such principle a priori, we demonstrate how such a picture arises in the worldline formulation of quantum field theory. Among other connections to holographic models, a warped ${\mathrm{AdS}}_5$ geometry, a quantum mechanical picture, and hidden local symmetry emerge, as well as a Wilson flow (gradient flow), which extends the four-dimensional sources to five-dimensional fields, and a link to the Gutzwiller trace formula. The worldline formulation also reproduces the nonrelativistic case, which is important for condensed-matter physics.

Figure 1

Some dominant diagrams. Double lines are for hadrons, single lines for quarks.