Strings, Junctions and Stability

Abstract

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 È 1 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.

Branes in hearts with perverse sheaves

“…Transforming the objects by the monodromy N times we can coerce the objects to be in the heart of the t-structure B, as marked in Figure 3(b). These will realize the spiral strings identified earlier [32].…”

“…These reproduce the the totality of states in the dyon spectrum of the Seiberg-Wittten theory both in the weak and the strong coupling regimes, which are identified as the regions outside and inside of the ellipse, respectively. The string junctions and spiral strings on the moduli space have also been identified among these stable objects [30,32].…”