In the first part of the talk, I will review recent techniques to prove that certain Euclidean Field Theories arise as high-density limits of interacting Bose gases at positive temperature. In the second part of the talk, I will present some new results that generalize these techniques to a trapping potential in dimension two, where a number of difficulties arise. Based on a joint work with Cristina Caraci, Antti Knowles, and Pedro Torres Giesteira. The Operator Algebra Seminar schedule is here: https://sites.google.com/view/oastorvergata/home-page