Target Space Duality I: General Theory

TL;DR

This paper develops a comprehensive classical framework for target space duality, revealing that dual manifolds are connected via a special symplectic manifold with a double fibration, unifying various duality types.

Contribution

It introduces a general geometric framework for target space duality, encompassing abelian, nonabelian, and Poisson-Lie dualities as special cases.

Findings

Dual manifolds are linked through a symplectic manifold with double fibration.

Both dual manifolds must have flat orthogonal connections.

New nonlinear dualities are demonstrated for the case M = Mtilde = R^n.

Abstract

We develop a systematic framework for studying target space duality at the classical level. We show that target space duality between manifolds M and Mtilde arises because of the existence of a very special symplectic manifold. This manifold locally looks like M x Mtilde and admits a double fibration. We analyze the local geometric requirements necessary for target space duality and prove that both manifolds must admit flat orthogonal connections. We show how abelian duality, nonabelian duality and Poisson-Lie duality are all special cases of a more general framework. As an example we exhibit new (nonlinear) dualities in the case M = Mtilde = R^n.