Instantons in nonlinear σ-models, gauge theories and general relativity

Abstract

We consider nonlinear σ-models, gauge theories and general relativity as three classes of models of field theory which are of an intrinsically geometric nature as well as (possibly) topologically nontrivial, and explore the role of instantons as the basic tool for new perturbative schemes in these models. In particular, we emphasize the close analogy between nonlinear σ-models and pure gauge theories. We also establish a new, manifest type of analogy by extending them to “nonlinear σ-models with gauge symmetry” and “pure gauge theories in a frame field formulation”, respectively.