On Global Analysis of Duality Maps

TL;DR

This paper provides a comprehensive analysis of duality maps in quantum field theories and string theories, identifying geometric conditions for duality existence and proposing extensions to non-abelian gauge theories.

Contribution

It introduces precise geometric conditions for duality existence and discusses the necessity of a new topological term in dual open string actions, extending duality analysis to non-abelian theories.

Findings

Duality exists only under specific geometric conditions.

A new topological term is required in dual open string actions.

Extension of duality construction to non-abelian gauge theories.

Abstract

A global analysis of duality transformations is presented. It is shown that duality between quantum field theories exists only when the geometrical structure of the quantum configuration spaces of the theories comply with certain precise conditions. Applications to S-dual actions and to T duality of string theories and D-branes are briefly discussed.It is shown that a new topological term in the dual open string actions is required. We also study an extension of the procedure to construct duality maps among abelian gauge theories to the non abelian case.