  We study false vacuum decay for a gauged complex scalar field in a polynomial
potential with nearly degenerate minima. Radiative corrections to the profile
of the nucleated bubble as well as the full decay rate are computed in the
planar thin-wall approximation using the effective action. This allows to
account for the inhomogeneity of the bounce background and the radiative
corrections in a self-consistent manner. In contrast to scalar or fermion
loops, for gauge fields one must deal with a coupled system that mixes the
Goldstone boson and the gauge fields, which considerably complicates the
numerical calculation of Green's functions. In addition to the renormalization
of couplings, we employ a covariant gradient expansion in order to
systematically construct the counterterm for the wave-function renormalization.
The result for the full decay rate however does not rely on such an expansion
and accounts for all gradient corrections at the chosen truncation of the loop
expansion. The ensuing gradient effects are shown to be of the same order of
magnitude as non-derivative one-loop corrections.
