The heights of rational points, and more generally of algebraic varieties defined over number fields, are real valued invariants which play an important role in arithmetic geometry. The work of Udi Hrushovski and Itaï Ben Yaacov on the model theory of globally valued fields « explains » the occurrence of these real valued invariants by relating them to continuous logic. In this talk, I will describe some further real invariants, the theta invariants, that also play a natural role in arithmetic geometry, and have direct relations with diverse other topics, notably lattice based cryptography and potential theory. This is joint work with François Charles.