The partition function of Ramond-Ramond p-form fields in Type IIA supergravity on a tenmanifold X contains subtle phase factors that are associated with T -duality, self-duality, and the relation of the RR fields to K-theory. The analogous partition function of M -theory on X × S 1 contains subtle phases that are similarly associated with E 8 gauge theory. We analyze the detailed phase factors on the two sides and show that they agree, thereby testing M -theory/Type IIA duality as well as the K-theory formalism in an interesting way. We also show that certain D-brane states wrapped on nontrivial homology cycles are actually unstable, that (−1) F L symmetry in Type IIA superstring theory depends in general on a cancellation between a fermion anomaly and an anomaly of RR fields, and thatType IIA superstring theory with no wrapped branes is well-defined only on a spacetime with W 7 = 0.

We study the correspondence between IIb solitonic 1-branes and monopoles in the context of the 3-brane realization of D = 4 N = 4 super Yang-Mills theory. We show that a bound state of 1-branes stretching between two separated 3-branes exhibits a family of supersymmetric ground states that can be identified with the ADHMN construction of the moduli space of SU (2) monopoles.. This identification is supported by the construction of the monopole gauge field as a space-time coupling in the quantum mechanical effective action of a 1-brane used as a probe. The analysis also reveals an intriguing aspect of the 1-brane theory: the transverse oscillations of the 1-branes in the ground states are described by non-commuting matrix valued fields which develop poles at the boundary. Finally, the construction is generalized to SU (n) monopoles with arbitrary n > 2.

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. ♮ diacones@sns.ias.edu ♯ jgomis@leland.stanford.edu 1 Some previous work on boundary states and orbifolds can be found in [8].proof of the McKay correspondence [13][14][15][16][17][18][19][20]. Roughly speaking, this correspondence states that there is a one-to-one correspondence between the number of non-trivial irreducible representations of the orbifold group Γ describing the isolated orbifold singularity C d /Γ and the homology generators of the crepant resolution of the singularity. In section 5 this will be explained in the more precise language of K-theory. In our physical situation, this follows from a deformation of the BPS spectrum determined by boundary states to the large radius limit of the orbifold moduli space where the states can be realized as D-branes wrapping supersymmetric cycles. We also analyze boundary states for certain non-isolated singularities and find that D-brane considerations suggest a generalization of the McKay correspondence to this case. This would relate non-trivial irreducible representations of the discrete group to compact homology generators of the resolved space.The reduced amount of supersymmetry of these vacua introduces corrections to the special geometry of the moduli space, which makes the abovementioned identification very difficult. In section 5 we work out an example by providing the exact solution for the C 3 /Z 3 model using the techniques of local mirror symmetry [21,22,23,24]. We identify the singularities in moduli space, the monodromies around these points and the exact central charge for the model. This allows us to make a precise identification between boundary states at the orbifold point with branes in the large volume limit. Moreover, the fractional branes at the orbifold are extended to an arbitrary point in moduli space. Similar results for the quintic moduli space have been obtained in [25]. The role of the perturbative orbifold point is played there by the Gepner point.The boundary state formalism serves very useful in analyzing the spectrum of models that do not have an obvious geometrical interpretation such as orbifolds with di...

We discuss the "fractional D-branes" which arise in orbifold resolution. We argue that they arise as subsectors of the Coulomb branch of the quiver gauge theory used to describe both string theory D-brane and Matrix theory on an orbifold, and thus must form part of the full physical Hilbert space. We make further observations confirming their interpretation as wrapped membranes.

We construct fractional branes in Landau-Ginzburg orbifold categories and study their behavior under marginal closed string perturbations. This approach is shown to be more general than the rational boundary state construction. In particular we find new D-branes on the quintic -such as a single D0-brane -which are not restrictions of bundles on the ambient projective space. We also exhibit a family of deformations of the D0-brane in the Landau-Ginzburg category parameterized by points on the Fermat quintic.