1 research outputs found
Equivariant Topological Sigma Models
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 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 anomaly explaining some problems with the formulation of
topological open string theory.Comment: 39 pages, 6 figures (available upon request); pure LaTeX file. [[The
paper was originally published as Prague preprint PRA-HEP-90/18 in December
1990. As the LaTeX file is still in demand, this is the original version with
just some minor changes and misprint corrections; a Note has been added to
update the state of the art.]