COVID-19 represents the most severe global crisis to date whose public conversation can be studied in real time. To do so, we use a data set of over 350 million tweets and retweets posted by over 26 million English speaking Twitter users from January 13 to June 7, 2020. We characterize the retweet network to identify spontaneous clustering of users and the evolution of their interaction over time in relation to the pandemic's emergence. We identify several stable clusters (super-communities), and are able to link them to international groups mainly involved in science and health topics, national elites, and political actors. The science- and health-related super-community received disproportionate attention early on during the pandemic, and was leading the discussion at the time. However, as the pandemic unfolded, the attention shifted towards both national elites and political actors, paralleled by the introduction of country-specific containment measures and the growing politicization of the debate. Scientific super-community remained present in the discussion, but experienced less reach and became more isolated within the network. Overall, the emerging network communities are characterized by an increased self-amplification and polarization. This makes it generally harder for information from international health organizations or scientific authorities to directly reach a broad audience through Twitter for prolonged time. These results may have implications for information dissemination along the unfolding of long-term events like epidemic diseases on a world-wide scale.