Equivariant Topological Sigma Models

Abstract

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 $C{P}^1\times C{P}^1$ 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.

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.]]

References in corpus (8)

• Holomorphic Anomalies in Topological Field Theories
• Mirror Manifolds And Topological Field Theory
• Batalin-Vilkovisky algebras and two-dimensional topological field theories
• Quantum Background Independence In String Theory
• Chern-Simons Gauge Theory on Orbifolds: Open Strings from Three Dimensions
• Topological Mirrors and Quantum Rings
• Two Dimensional String Theory and the Topological Torus
• Spacetime Diffeomorphisms and Topological W-Infinity Symmetry in Two Dimensional Topological String Theory

Cited by in corpus (23)

• D-Branes And K-Theory
• Toroidal Compactification Without Vector Structure
• K3 Orientifolds
• Strings on Orientifolds
• Chern-Simons Gauge Theory As A String Theory
• T-duality for open strings
• Orientifolding the conifold
• Some Comments on Branes, G-flux, and K-theory
• Type IIA D-Branes, K-Theory, and Matrix Theory
• Topological Rigid String Theory and Two Dimensional QCD
• Chern-Simons Gauge Theory on Orbifolds: Open Strings from Three Dimensions
• D-branes in Orbifold Singularities and Equivariant K-Theory
• N=1 Type IIA brane configurations, Chirality and T-duality
• Evidence for Tadpole Cancellation in the Topological String
• Type IIB Orientifolds without Untwisted Tadpoles, and non-BPS D-branes
• Orientifolds, Unoriented Instantons and Localization
• Constructing D-Branes from K-Theory
• Closed and open conformal field theories and their anomalies
• Chern-Simons from Dirichlet 2-brane instantons
• From Boundaries To Conditions Over Superspace
• Tropological Sigma Models
• Open/Closed Topological CP1 Sigma Model Revisited
• Towards quantum cohomology of real varieties