String Theory Journal Club

I will demonstrate that wall-crossing behaviour of framed BPS states in N=4 and N=2 four-dimensional supersymmetric gauge theories can be described using a new and powerful algebraic formalism. In particular, I show that the algebra of line operators is given by the image of the "universal" algebra (quantum affine or quantum toroidal) in a tensor product of certain particularly simple representations thereof. The action of the "universal" algebra on the tensor product requires the choice of the coproduct, which turns out not to be unique, but is parametrized by chambers in the moduli space of the gauge theory. Different choices of coproduct are related by Drinfeld twists, each given by the product of certain elementary twists corresponding to walls of the second kind in the moduli space. The Kontsevich-Soibelman spectrum generator is then given by the R-matrix of the "universal" algebra.