Duality on Higher Order U(1) Bundles

TL;DR

This paper introduces a global geometric framework for duality transformations using higher order U(1) bundles, providing a topological interpretation of charges and establishing quantum equivalence between dual theories.

Contribution

It generalizes complex line bundle structures to higher order U(1) bundles and formulates duality maps over these, with a global constraint ensuring well-defined bundles.

Findings

Quantum equivalence between dual theories established.

Refined proof of duality between supermembranes with topological interpretation.

Global structures necessary for well-defined higher order bundles.

Abstract

A new global approach in the study of duality transformations is introduced. The geometrical structure of complex line bundles is generalized to higher order U(1) bundles which are classified by quantized charges and duality maps are formulated over these structures. Quantum equivalence is shown between dual theories. A global constraint is proven to be needed to achieve well defined bundles. These global structures are used to refine the proof of the duality equivalence between d=11 supermembrane and d=10 IIA Dirichlet supermembrane, giving a complete topological interpretation to their quantized charges.