Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-10-16
Rev.Math.Phys.21:1091-1143,2009
Physics
High Energy Physics
High Energy Physics - Theory
40 pages; v4: Clarifying comments added, more detailed proof of main isomorphism theorem given; Final version to be published
Scientific paper
10.1142/S0129055X09003839
We study the classification of D-branes and Ramond-Ramond fields in Type I string theory by developing a geometric description of KO-homology. We define an analytic version of KO-homology using KK-theory of real C*-algebras, and construct explicitly the isomorphism between geometric and analytic KO-homology. The construction involves recasting the Cl(n)-index theorem and a certain geometric invariant into a homological framework which is used, along with a definition of the real Chern character in KO-homology, to derive cohomological index formulas. We show that this invariant also naturally assigns torsion charges to non-BPS states in Type I string theory, in the construction of classes of D-branes in terms of topological KO-cycles. The formalism naturally captures the coupling of Ramond-Ramond fields to background D-branes which cancel global anomalies in the string theory path integral. We show that this is related to a physical interpretation of bivariant KK-theory in terms of decay processes on spacetime-filling branes. We also provide a construction of the holonomies of Ramond-Ramond fields in Type II string theory in terms of topological K-chains.
Reis Rui M. G.
Szabo Richard J.
Valentino Alessandro
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