We study the phase diagram of a resistively shunted Josephson junction (RSJJ) in the framework of the boundary sine-Gordon model. Using the non-perturbative functional renormalization group (FRG) we find that the transition is not controlled by a single fixed point but by a line of fixed points, and compute the continuously varying critical exponent $ν$. We argue that the conductance also varies continuously along the transition line. In contrast to the traditional phase diagram of the RSJJ -- an insulating ground state when the shunt resistance $R$ is larger than $R_q=h/(2e)^2$ and a superconducting one when $R

15 pages, 15 figures ; v2 closer to published version