  We discuss the stability of a homogeneous two-dimensional Bose gas at finite
temperature against formation of isolated vortices. We consider a patch of
several healing lengths in size and compute its free energy using the Euclidean
formalism. Since we deal with an open system, which is able to exchange
particles and angular momentum with the rest of the condensate, we use the
symmetry-breaking (as opposed to the particle number conserving) formalism, and
include configurations with all values of angular momenta in the partition
function. At finite temperature, there appear sphaleron configurations
associated to isolated vortices. The contribution from these configurations to
the free energy is computed in the dilute gas approximation. We show that the
Euclidean action of linearized perturbations of a vortex is not positive
definite. As a consequence the free energy of the 2D Bose gas acquires an
imaginary part. This signals the instability of the gas. This instability may
be identified with the Berezinskii, Kosterlitz and Thouless (BKT) transition.
