Shadow sectors of gauge theories

TL;DR

Shadow charges reveal infrared sectors of gauge theories by treating static Gauss-law deformations $\rho(x)$ as genuine, gauge-invariant initial data. The authors develop a BRST framework, including an orbit-BRST extension for second-class constraints, to define a gauge-invariant reduced phase space and to compute observables without introducing ultraviolet degrees of freedom. In QED, shadow charges correspond to coherent states of the longitudinal electric field and unphysical modes decouple via the quartet mechanism; in non-Abelian theories, shadow charges are quantized and described either with UV-heavy fields or via the constraint orbit, yielding equivalent physical predictions. Overall, the work shows that every local conservation law gives rise to a gauge symmetry in an extended phase space, allowing soft Lorentz breaking and offering new insights into the infrared structure of gauge theories and potential connections to gravity.

Abstract

We show that both abelian and non-abelian gauge theories admit configurations in which the fields behave as if in the presence of static charge densities, or ``shadow charges". These correspond to nontrivial initial conditions for the fields that generate gauge transformations, the Gauss' law operators. In non-abelian theories, such configurations seem to demand additional physical fields with exactly static charge densities. In contrast with this expectation, we show that gauge theory alone provides a consistent and gauge-invariant description of shadow charges. Canonical quantization then yields continuous shadow charges for abelian theories and quantized ones for non-abelian theories. In general, our findings indicate that all local conservation laws give rise to gauge symmetries, even in the presence of second-class constraints.