The Brownian loop soup in some two-dimensional domain is a random collection of infinitely many Brownian-type loops. It is sampled according to theta times a certain loop measure, where theta > 0 is a parameter of the model. First introduced by Lawler and Werner, it has become a central object of study in random conformal geometry, in particular due to its connections with conformal loop ensembles (CLE) and the Gaussian free field (GFF). This latter connection, referred to as Le Jan?s isomorphism, states that, when theta = 1/2, the occupation field of the loop soup has the same law as the square of a GFF. Remarkably, it is even possible to fully recover the GFF (also its sign) out of the Brownian loop soup with the help of additional coin tosses (Lupu and Aru?Lupu?Sepulveda). The main goal of this talk is to answer the following question: What is the field naturally associated to the loop soup when theta < 1/2? Along the way, we will have to study the percolative properties of the loop soup.