Massless D-Branes on Calabi-Yau Threefolds and Monodromy

We analyze the link between the occurrence of massless B-type D-branes for specific values of moduli and monodromy around such points in the moduli space. This allows us to propose a classification of all massless B-type D-branes at any point in the moduli space of Calabi-Yau's. This classification then justifies a previous conjecture due to Horja for the general form of monodromy. Our analysis is based on using monodromies around points in moduli space where a single D-brane becomes massless to generate monodromies around points where an infinite number become massless. We discuss the various possibilities within the classification.Comment: 29 pages, LaTeX2e, 3 figures, author order fixe

On the Geometric Interpretation of N = 2 Superconformal Theories

We clarify certain important issues relevant for the geometric interpretation of a large class of N = 2 superconformal theories. By fully exploiting the phase structure of these theories (discovered in earlier works) we are able to clearly identify their geometric content. One application is to present a simple and natural resolution to the question of what constitutes the mirror of a rigid Calabi-Yau manifold. We also discuss some other models with unusual phase diagrams that highlight some subtle features regarding the geometric content of conformal theories.Comment: 25 pages, note adde

Small Volumes in Compactified String Theory

We discuss some of the classical and quantum geometry associated to the degeneration of cycles within a Calabi-Yau compactification. In particular, we focus on the definition and properties of quantum volume, especially as it applies to identifying the physics associated to loci in moduli space where nonperturbative effects become manifest. We discuss some unusual features of quantum volume relative to its classical counterpart.Comment: 22 pages, 5 eps figures, harvma

D-Brane Topology Changing Transitions

We study D-branes on three-dimensional orbifold backgrounds that admit topologically distinct resolutions differing by flop transitions. We show that these distinct phases are part of the vacuum moduli space of the super Yang-Mills gauge theory describing the D-brane dynamics. In this way we establish that D-branes --- like fundamental strings --- allow for physically smooth topology changing transitions.Comment: 16 pages, 3 figures, Harvma

Non-Simply-Connected Gauge Groups and Rational Points on Elliptic Curves

We consider the F-theory description of non-simply-connected gauge groups appearing in the E8 x E8 heterotic string. The analysis is closely tied to the arithmetic of torsion points on an elliptic curve. The general form of the corresponding elliptic fibration is given for all finite subgroups of E8 which are applicable in this context. We also study the closely-related question of point-like instantons on a K3 surface whose holonomy is a finite group. As an example we consider the case of the heterotic string on a K3 surface having the E8 gauge symmetry broken to (E6 x SU(3))/Z3 or SU(9)/Z3 by point-like instantons with Z3 holonomy.Comment: 15 pages, 2 embedded figures, some spurious U(1)'s remove

Orbifold Resolution by D-Branes

We study topological properties of the D-brane resolution of three-dimensional orbifold singularities, C^3/Gamma, for finite abelian groups Gamma. The D-brane vacuum moduli space is shown to fill out the background spacetime with Fayet--Iliopoulos parameters controlling the size of the blow-ups. This D-brane vacuum moduli space can be classically described by a gauged linear sigma model, which is shown to be non-generic in a manner that projects out non-geometric regions in its phase diagram, as anticipated from a number of perspectives.Comment: 26 pages, 2 figures (TeX, harvmac big, epsf

D-branes and Discrete Torsion II

We derive D-brane gauge theories for C^3/Z_n x Z_n orbifolds with discrete torsion and study the moduli space of a D-brane at a point. We show that, as suggested in previous work, closed string moduli do not fully resolve the singularity, but the resulting space -- containing n-1 conifold singularities -- is somewhat surprising. Fractional branes also have unusual properties. We also define an index which is the CFT analog of the intersection form in geometric compactification, and use this to show that the elementary D6-brane wrapped about T^6/Z_n x Z_n must have U(n) world-volume gauge symmetry.Comment: harvmac, 25 p

Chiral Rings Do Not Suffice: N=(2,2) Theories with Nonzero Fundamental Group

The Kahler moduli space of a particular non-simply-connected Calabi-Yau manifold is mapped out using mirror symmetry. It is found that, for the model considered, the chiral ring may be identical for different associated conformal field theories. This ambiguity is explained in terms of both A-model and B-model language. It also provides an apparent counterexample to the global Torelli problem for Calabi-Yau threefolds.Comment: 12 page