Gravity with more or less gauging

General Relativity is conventionally formulated as a theory with gauge invariance under the diffeomorphism group of general coordinate transformations, but there are locally equivalent formulations in terms of either a larger (additional local conformal invariance) or smaller (only “special” diffeomorphisms) group of symmetries. Other formulations with the same number of gauge generators, but a different gauge algebra, also exist. We will discuss how one can relate these different formulations to each other, and illustrate various applications in which one may prefer one or another formalism. (The talk is mostly based on arXiv:1805.11626.)