IAS Physics Group Meeting
2-Categories and the Massive 3d A-Model
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Abstract: Let Z be a hyperKahler manifold admitting a U(1) hyperKahler isometry. There is a three-dimensional sigma model with eight supercharges, with target space Z and potential determined by the hyperKahler moment map. The theory admits half-BPS domain walls, quarter-BPS domain wall junctions and one-eighth BPS intersections of domain wall junctions. I will describe how such networks of domain walls can be organized into a novel algebraic structure: an A-infinity 2-category. I will build up to this structure gradually, describing first what happens in dimension one (Morse theory) and two (the Gaiotto-Moore-Witten formalism).