Symmetries play a key role in theoretical physics. But in Nature, most realistic systems do not possess it. However, if we go far away from a source (electric charge or a massive object), the spacetime becomes approximately empty and flat, and we can talk about asymptotic symmetries.

The goal of this work is to understand a relation between the asymptotic symmetries and its classically observable counterpart, the memory effect. This phenomenon was first studied in the context of gravitational waves by Zel’dovich and Polnarev and has subsequently been developed by others. To gain better physical understanding of the problem, we focus on analogous electromagnetic memory effect of radiation proposed recently, which is much simpler. A purpose of my present exploration is to gain understanding of this effect within the context of three-dimensional gravitational theory invariant under extended group of local symmetries which possesses richer asymptotic structure. Thus, we expect that its memory effect will distinguish this theory from general relativity.