Constructing D-Branes from K-Theory

TL;DR

This paper reviews how topological K-theory classifies D-branes in superstring theory, explaining recent advances, new interpretations, and predictions of D-brane spectra and relationships between string theories.

Contribution

It provides a comprehensive review of the application of K-theory to D-branes, including new insights into their classification, spectra, and dualities in superstring theory.

Findings

K-theory reproduces known D-brane spectra

Predicts new D-brane states and relationships

Connects K-theory with string dualities

Abstract

A detailed review of recent developments in the topological classification of D-branes in superstring theory is presented. Beginning with a thorough, self-contained introduction to the techniques and applications of topological K-theory, the relationships between the classic constructions of K-theory and the recent realizations of D-branes as tachyonic solitons, coming from bound states of higher dimensional systems of unstable branes, are described. It is shown how the K-theory formalism naturally reproduces the known spectra of BPS and non-BPS D-branes, and how it can be systematically used to predict the existence of new states. The emphasis is placed on the new interpretations of D-branes as conventional topological solitons in other brane worldvolumes, how the mathematical formalism can be used to deduce the gauge field content on both supersymmetric and non-BPS branes, and also how K-theory predicts new relationships between the various superstring theories and their D-brane spectra. The implementations of duality symmetries as natural isomorphisms of K-groups are discussed. The relationship with the standard cohomological classification is presented and used to derive an explicit formula for D-brane charges. Some string theoretical constructions of the K-theory predictions are also briefly described.