Deciphering the unusual stellar progenitor of GRB~210704A

GRB~210704A is a burst of intermediate duration ($T_{90} \sim 1-4$~s) followed by a fading afterglow and an optical excess that peaked about 7 days after the explosion. Its properties, and in particular those of the excess, do not easily fit into the well established classification scheme of GRBs as being long or short, leaving the nature of its progenitor uncertain. We present multi-wavelength observations of the GRB and its counterpart, observed up to 160 days after the burst. In order to decipher the nature of the progenitor system, we present a detailed analysis of the GRB high-energy properties (duration, spectral lag, and Amati correlation), its environment, and late-time optical excess. We discuss three possible scenarios: a neutron star merger, a collapsing massive star, and an atypical explosion possibly hosted in a cluster of galaxies. We find that traditional kilonova and supernova models do not match well the properties of the optical excess, leaving us with the intriguing suggestion that this event was an exotic high-energy merger.