Classical Geometry and Target Space Duality

TL;DR

This paper introduces a new formulation of restricted target space duality in classical two-dimensional nonlinear sigma models, linking it to classical differential geometry without requiring target space symmetry.

Contribution

It presents a novel local theory framework for restricted target space duality, extending the understanding beyond symmetric target spaces.

Findings

Establishes an analogy between Euclidean and Riemannian geometry and their dualities.

Identifies restricted target space duality with a problem in classical differential geometry.

Provides a local theoretical approach to duality without symmetry constraints.

Abstract

This is the written version of lectures presented at Cargese 95. A new formulation for a ``restricted'' type of target space duality in classical two dimensional nonlinear sigma models is presented. The main idea is summarized by the analogy: euclidean geometry is to riemannian geometry as toroidal target space duality is to ``restricted'' target space duality. The target space is not required to possess symmetry. These lectures only discuss the local theory. The restricted target space duality problem is identified with an interesting problem in classical differential geometry.