Lagrangian pairs of pants

We construct a Lagrangian submanifold, inside the cotangent bundle of a real torus, which we call a Lagrangian pair of pants. It is given as the graph of an exact one form defined on the real blow up of a Lagrangian coamoeba. Lagrangian pairs of pants are the main building blocks in a construction of smooth Lagrangian submanifolds of $(mathbbC^*)^n$ which lift tropical subvarieties in $mathbbR^n$. As an example we explain how to lift tropical curves in $mathbbR^2$ to Lagrangian submanifolds of $(mathbbC^*)^2$. We also give several new examples of Lagrangian submanifolds inside toric varieties, some of which are monotone.