Description
We study BPS structures in a class of 4d N=2 theories that can be
realised in type IIB string theory on a Calabi-Yau 3-fold.
The number of BPS states in these theories jumps discontinuously at
special loci in the moduli space called walls of marginal stability.
We use attractor flow methods to determine the BPS spectrum in each
chamber bounded by these walls in several cases including the
Argyres-Douglas A_2 model and pure SU(2) Seiberg-Witten theory. This is
done by looking at existence conditions on the endpoints
of the gradient flow lines of the BPS central charges and by considering
that flow lines can split at the walls where the composite
BPS states decay into their constituents. This involves first finding
the central charges of the BPS states as linear combinations
of periods associated to an elliptic curve embedded in the Calabi-Yau
3-fold. These are periods of a meromorphic differential and
are derived by solving the appropriate Picard-Fuchs equations.
