Discovery of a persistent radio source associated with FRB 20240114A

Aims. We present the discovery of a fourth persistent radio source (PRS) associated with a fast radio burst (FRB). Methods. Following previous indications of a candidate PRS associated with FRB 20240114A, we performed deep Very Long Baseline Array observations at 5 GHz to test the presence of a compact radio source within the uncertainty position of this FRB (+/- 200 mas). Results. We detected a component similar to 50 mas northwards of the nominal position provided by the PRECISE collaboration. The corresponding radio luminosity together with the Faraday rotation measure provided by previous observations of the FRB locate this PRS in the expected region of the radio luminosity versus Faraday rotation measure relation for the nebular model, further supporting its validity. Comparison of the measured flux density with the values collected at a lower frequency by previous studies indicates a possible steepening of the radio spectrum in the 1-5 GHz range. Optical observations performed with the Large Binocular Telescope could reveal that the FRB and its PRS lie at similar to 1 kpc from the centre of the host galaxy, which is a dwarf sub-solar metallicity starburst galaxy with a star-formation rate of similar to 1 M-circle dot yr(-1) and a stellar mass of M similar to 10(8) M-circle dot.