Notes on Certain (0,2) Correlation Functions

Details Notes on Certain (0,2) Correlation Functions Notes on Certain (0,2) Correlation Functions

2004-06-24

arxiv.org/abs/hep-th/0406226v3

Commun.Math.Phys. 262 (2006) 611-644

Physics

High Energy Physics

High Energy Physics - Theory

51 pages, LaTeX; v2: typos fixed; v3: more typos fixed

Scientific paper

10.1007/s00220-005-1443-1

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 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.

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