Equivariant Topological Sigma Models

Details Equivariant Topological Sigma Models Equivariant Topological Sigma Models

1993-09-22

arxiv.org/abs/hep-th/9309124v1

Nucl.Phys. B418 (1994) 571-602

Physics

High Energy Physics

High Energy Physics - Theory

39 pages, 6 figures (available upon request); pure LaTeX file. [[The paper was originally published as Prague preprint PRA-HEP

Scientific paper

10.1016/0550-3213(94)90531-2

We identify and examine a generalization of topological sigma models suitable for coupling to topological open strings. The targets are Kahler manifolds with a real structure, i.e. with an involution acting as a complex conjugation, compatible with the Kahler metric. These models satisfy axioms of what might be called ``equivariant topological quantum field theory,'' generalizing the axioms of topological field theory as given by Atiyah. Observables of the equivariant topological sigma models correspond to cohomological classes in an equivariant cohomology theory of the targets. Their correlation functions can be computed, leading to intersection theory on instanton moduli spaces with a natural real structure. An equivariant $CP^1\times CP^1$ model is discussed in detail, and solved explicitly. Finally, we discuss the equivariant formulation of topological gravity on surfaces of unoriented open and closed string theory, and find a $Z_2$ anomaly explaining some problems with the formulation of topological open string theory.

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