Fractional Branes and Boundary States in Orbifold Theories

TL;DR

This paper investigates the spectrum of D-branes in N=2 string orbifold theories using boundary states, comparing results with K-theory predictions and exploring their geometric interpretation in the large radius limit.

Contribution

It provides a detailed boundary state construction for various orbifolds, generalizes K-theoretic classifications, and links fractional branes to vector bundles on exceptional cycles.

Findings

Results agree with K-theory predictions where available.

Constructs boundary states for orbifolds with singularities and discrete torsion.

Establishes a correspondence between fractional branes and vector bundles on P^2.

Abstract

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.