Strings, Junctions and Stability

Identification of string junction states of pure SU(2) Seiberg-Witten theory as B-branes wrapped on a Calabi-Yau manifold in the geometric engineering limit is discussed. The wrapped branes are known to correspond to objects in the bounded derived category of coherent sheaves on the projective line P1 in this limit. We identify the pronged strings with triangles in the underlying triangulated category using Π-stability. The spiral strings in the weak coupling region are interpreted as certain projective resolutions of the invertible sheaves. We discuss transitions between the spiral strings and junctions using the grade introduced for Π-stability through the central charges of the corresponding objects. [email protected] [email protected] [email protected]