  In this note we show that the 2D continuum Gaussian free field (GFF) admits
an excursion decomposition that is on the one hand similar to the classical
excursion decomposition of the Brownian motion, and on the other hand can be
seen as an FK representation of the continuum GFF. In particular, 2D continuum
GFF can be written as an infinite sum of disjoint positive and negative sign
excursions, which are given by Minkowski content measures of clusters of a
critical 2D Brownian loop soup with i.i.d. signs. Although the 2D continuum GFF
is not even a signed measure, we show that the decomposition to positive and
negative parts is unique under natural conditions.
