The fifth dimension in the worldline formalism, holography, and the Wilson flow

Abstract

We develop a model for hadrons in the framework of the worldline formalism. While being based wholly in four-dimensional quantum field theory, it shares many features with holographic approaches: Already by the use of the worldline formalism the approach appears intrinsically quantum mechanical. As auxiliary fifth dimension Schwinger's proper time is grouped with the physical four spacetime dimensions into an ${\mathrm{AdS}}_{5}$ geometry, which is warped due to conformal-symmetry breaking effects. Hidden local symmetry is emergent. The four-dimensional sources are extended to five-dimensional fields by a Wilson flow (gradient flow). A variational principle for the flow reproduces exactly the corresponding holographic computation. The worldline approach also yields the higher-dimensional description in the nonrelativistic case.