Physics-informed gauge theories

Abstract

We use the physics-informed renormalisation group (PIRG) for the construction of gauge invariant renormalisation group flows. The respective effective action is a sum of a gauge invariant quantum part and the classical gauge fixing part which arranges for invertibility of the gauge field two-point function. Thus, the BRST transformations simply accommodate the gauge consistency of the gauge fixing sector, while the quantum part of the effective action is gauge and BRST invariant. We apply this physics-informed approach to Yang-Mills theory and gravity and show how the flowing gauge fields arrange for full gauge invariance. We also embed the background field approximation to the functional renormalisation group (fRG) in an exact gauge invariant PIRG flow. This allows us to discuss the dynamics of the correction terms, and the non-trivial ultraviolet or infrared relevant terms are elucidated within a one-loop approximation. The background field approximation of the latter is known for violating one-loop universality for specific regulators and we show how the present setup reinstates universality in a constructive way. Finally, we discuss the landscape of fRG flows in gauge theories through the lens of the novel PIRG approach as well as potential applications.