Spacetime Topology, Conserved Charges, and the Splitting of Classical Multiplets

TL;DR

This paper explores how non-trivial spacetime topology affects conserved charges, symmetry structures, and multiplet splitting in string theory and supergravity, using advanced geometric and algebraic methods.

Contribution

It introduces topological extensions of Noether charges, extends isometry groups to semigroups, and describes multiplet splitting via symplectic geometry in multiply-connected phase spaces.

Findings

Topological extensions of Noether charges for D-branes.

Extension of isometry groups to semigroups in lightlike compactifications.

Description of classical multiplet splitting using symplectic covering spaces.

Abstract

We examine consequences of non-trivial topology in background spacetimes and super-spacetimes: It is shown how the semi-invariance of a brane Lagrangian under supertranslations gives rise to topological extensions of the Noether charge algebra carried by D-branes. We investigate how isometry groups of lightlike compactified spacetimes admit an extension to a semigroup. It is shown how the splitting of classical multiplets caused by multiply-connectedness of a phase space can be described in the framework of Symplectic Geometry, based on the concept of symplectic covering spaces and local moment maps.