Topological σ-model, Hamiltonian dynamics and loop space Lefschetz number

ar X iv : h ep - t h / 95 08 06 7 v 2 1 8 Ju l 1 99 6 hep - th / 9508067 TOPOLOGICAL σ - MODEL , HAMILTONIAN DYNAMICS AND LOOP SPACE LEFSCHETZ NUMBER

We use path integral methods and topological quantum field theory techniques to investigate a generic classical Hamiltonian system. In particular, we show that Floer’s instanton equation is related to a functional Euler character in the quantum cohomology defined by the topological nonlinear σ–model. This relation is an infinite dimensional analog of the relation between Poincaré–Hopf and Gauss...

Symmetric Space σ-model Dynamics: Current Formalism

After explicitly constructing the symmetric space sigma model lagrangian in terms of the coset scalars of the solvable Lie algebra gauge in the current formalism we derive the field equations of the theory.

σ-Normality of Topological Spaces

3-dimensional topological σ-model ∗

A 3-dimensional model dual to the Rozansky-Witten topological sigma-model with a hyper-Kähler target space is considered. It is demonstrated that a Feynman diagram calculation of the classical part of its partition function yields the Milnor linking number.

Symmetric Space σ-model Dynamics: Internal Metric Formalism

For the symmetric space sigma model in the internal metric formalism we explicitly construct the lagrangian in terms of the axions and the dilatons of the solvable Lie algebra gauge and then we exactly derive the axion-dilaton field equations.