Constructing D-Branes from K-Theory

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.

112 pages LaTeX, 1 .eps file, uses epsf.tex; Run 3 times to generate table of contents properly; Typos corrected

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Cited by in corpus (14)

• Proposal for non-BPS D-brane action
• A Derivation of K-Theory from M-Theory
• T-Duality, and the K-Theoretic Partition Function of TypeIIA Superstring Theory
• Dyons, K-theory and M-theory
• Brane Descent Relations in M-theory
• D-Branes in Type IIA and Type IIB Theories from Tachyon Condensation
• Topics on D-brane charges with B-fields
• Remark about Non-BPS D-Brane in Type IIA Theory
• Lectures on Strings, D-branes and Gauge Theories
• Matrix Model and String Field Theory
• Projective resolutions of coherent sheaves and descent relations between branes
• Exotic smooth R^4, geometry of string backgrounds and quantum D-branes
• D-Branes, AdS/CFT Correspondence, and T-Duality
• K-Theory and Gauge Solitons