A Vertex Formalism for Local Ruled Surfaces

We develop a vertex formalism for topological string amplitudes on ruled surfaces with an arbitrary number of reducible fibers embedded in a Calabi-Yau threefold. Our construction is based on large N duality and localization with respect to a degenerate torus action. We also discuss potential generalizations of our formalism to a broader class of Calabi-Yau threefolds using the same underlying principles.Comment: 24 pages, 12 figures; v2: minor changes; v3: explanations added, results unchange

Neveu-Schwarz Five-Branes And Matrix String Theory On K3

The Matrix theory description of Type IIA string theory on a compact K3 surface as the theory of Neveu-Schwarz five-branes on $\tilde{K3}\times S^1$ is analyzed. The full multiplet of space-time BPS states is identified in the five-brane world-volume as fluxes.Comment: harvmac, 12 pages, some changes in the T-duality on K3 sectio

Fractional Branes and Boundary States in Orbifold Theories

We study the D-brane spectrum of N=2 string orbifold theories using the boundary state formalism. The construction is carried out for orbifolds with isolated singularities, non-isolated singularities and orbifolds with discrete torsion. Our results agree with the corresponding K-theoretic predictions when they are available and generalize them when they are not. This suggests that the classification of boundary states provides a sort of "quantum K-theory" just as chiral rings in CFT provide "quantum" generalizations of cohomology. We discuss the identification of these states with D-branes wrapping holomorphic cycles in the large radius limit of the CFT moduli space. The example C^3/Z_3 is worked out in full detail using local mirror symmetry techniques. We find a precise correspondence between fractional branes at the orbifold point and configurations of D-branes described by vector bundles on the exceptional P^2 cycle.Comment: 48 pages, Harvmac, 3 postscript figures, references and a note adde

The Coulomb Branch of (4,4) Supersymmetric Field Theories in Two Dimensions

We study (4,4) supersymmetric field theories in two dimensions with a one dimensional Coulomb branch. These theories have applications in string theory. Our analysis explains the known relation between $A-D-E$ groups and modular invariants of affine SU(2).Comment: 18 pages, minor change