Field-dependent diffeomorphisms and the transformation of surface charges between gauges

A bstract When studying gauge theories in the presence of boundaries, local symmetry transformations are typically classified as gauge or physical depending on whether the associated charges vanish or not. Here, we propose that physical charges should further be refined into “dynamical” or “kinematical” depending on whether they are associated with evolution equations or not. To support this proposal, we analyze (A)dS 3 gravity with boundary Weyl rescalings and compare the solution spaces in Bondi-Sachs and Fefferman- Graham coordinates. In line with previous accounts, we show that the Weyl charge vanishes in the Bondi-Sachs gauge but not in the Fefferman-Graham gauge. Conversely, the charges arising from the metric Chern-Simons Lagrangian behave in the opposite way. This indicates that the gauge-dependent Weyl charge differs fundamentally from charges like mass and angular momentum. This interpretation is reinforced by two key observations: the Weyl conformal factor does not satisfy any evolution equation, and the associated charge arises from a corner term in the symplectic structure. These properties justify assigning the Weyl charge a kinematical status. These results can also be derived using the field-dependent diffeomorphism that maps between the two gauges. Importantly, this diffeomorphism does not act tensorially on the variational bi-complex due to its field dependency, and is able to “toggle” charges on or off. This provides an example of a large diffeomorphism between gauges, as opposed to a residual diffeomorphism within a gauge.