Projector Equivalences in K theory and Families of Non-commutative Solitons

TL;DR

This paper explores how projector equivalences in K-theory lead to new solution-generating techniques for non-commutative solitons, enabling the construction of dynamic and interpolating solutions relevant to string theory and brane physics.

Contribution

It introduces a generalization of the soliton solution method in non-commutative field theories using K-theoretic projector equivalences, extending to time-dependent and interpolating solutions.

Findings

Generalized solution techniques for non-commutative solitons.

Construction of time-dependent and interpolating solutions.

Insights into the topology of string field configuration space.

Abstract

Projector equivalences used in the definition of the K-theory of operator algebras are shown to lead to generalizations of the solution generating technique for solitons in NC field theories, which has recently been used in the construction of branes from other branes in B-field backgrounds and in the construction of fluxon solutions of gauge theories. The generalizations involve families of static solutions as well as solutions which depend on euclidean time and interpolate between different configurations. We investigate the physics of these generalizations in the brane-construction as well as the fluxon context. These results can be interpreted in the light of recent discussions on the topology of the configuration space of string fields.