Algebra of the Infrared with Twisted Masses

The Gaiotto-Moore-Witten "Algebra of the Infrared" allows one to construct the category of supersymmetric boundary conditions for a wide class of massive N=(2,2) QFTs in two dimensions. In particular, it applies to N=(2,2) QFTs defined by a Morse superpotential W. However, the formalism breaks down if we consider an N=(2,2) QFT with a non-trivial twisted mass, or if the one-form dW is not globally exact and has a non-trivial period. Many of the N=(2,2) QFTs of interest are exactly of this type. In this talk I will show how one can generalize the GMW framework to include such models, illustrating the basic idea in a simple toy model.