In this paper, we will discuss gauged linear sigma model descriptions of toric stacks. Toric stacks have a simple description in terms of (symplectic, GIT) C × quotients of homogeneous coordinates, in exactly the same form as toric varieties. We describe the physics of the gauged linear sigma models that formally coincide with the mathematical description of toric stacks and check that physical predictions of those gauged linear sigma models exactly match the corresponding stacks. We also see in examples that when a given toric stack has multiple presentations in a form accessible as a gauged linear sigma model, that the IR physics of those different presentations matches, so that the IR physics is presentation-independent, making it reasonable to associate CFTs to stacks, not just presentations of stacks. We discuss mirror symmetry for stacks, using MorrisonPlesser-Hori-Vafa techniques to compute mirrors explicitly, and also find a natural generalization of Batyrev's mirror conjecture. In the process of studying mirror symmetry, we find some new abstract CFTs, involving fields valued in roots of unity. e-print archive: http://lanl.arXiv.org/abs/hep-th/0502053 TONY PANTEV AND ERIC SHARPE

We continue our study of heterotic compactifications on non-Kähler complex manifolds with torsion. We give further evidence of the consistency of the six-dimensional manifold presented earlier and discuss the anomaly cancellation and possible supergravity description for a generic non-Kähler complex manifold using the newly proposed superpotential. The manifolds studied in our earlier papers had zero Euler characteristics. We

In this paper we shall describe some correlation function computations in perturbative heterotic strings that, for example, in certain circumstances can lend themselves to a heterotic generalization of quantum cohomology calculations. Ordinary quantum chiral rings reflect worldsheet instanton corrections to correlation functions involving products of elements of Dolbeault cohomology groups on the target space. The heterotic generalization described here involves computing worldsheet instanton corrections to correlation functions defined by products of elements of sheaf cohomology groups. One must not only compactify moduli spaces of rational curves, but also extend a sheaf (determined by the gauge bundle) over the compactification, and linear sigma models provide natural mechanisms for doing both. Euler classes of obstruction bundles generalize to this language in an interesting way.

In this note we explicitly work out the precise relationship between Ext groups and massless modes of D-branes wrapped on complex submanifolds of Calabi-Yau manifolds. Specifically, we explicitly compute the boundary vertex operators for massless Ramond sector states, in open string B models describing Calabi-Yau manifolds at large radius, directly in BCFT using standard methods. Naively these vertex operators are in one-to-one correspondence with certain sheaf cohomology groups (as is typical for such vertex operator calculations), which are related to the desired Ext groups via spectral sequences. However, a subtlety in the physics of the open string B model has the effect of physically realizing those spectral sequences in BUST cohomology, so that the vertex operators are actually in one-to-one correspondence with Ext group elements. This gives an extremely concrete physical test of recent proposals regarding the relationship between derived categories and D-branes. We check these results extensively in numerous examples, and comment on several related issues. e-print archive: http://laiil.arXiv.org/abs/hep-th/0208104

In this technical note we give a purely geometric understanding of discrete torsion, as an analogue of orbifold Wilson lines for two-form tensor field potentials. In order to introduce discrete torsion in this context, we describe gerbes and the description of certain type II supergravity tensor field potentials as connections on gerbes. Discrete torsion then naturally appears in describing the action of the orbifold group on (1-)gerbes, just as orbifold Wilson lines appear in describing the action of the orbifold group on the gauge bundle. Our results are not restricted to trivial gerbes -in other words, our description of discrete torsion applies equally well to compactifications with nontrivial H-field strengths. We also describe a specific program for rigorously deriving analogues of discrete torsion for many of the other type II tensor fields, and we are able to make specific conjectures for the results.