Heriot-Watt Mathematics Report Series
HWM06-40, 13 Oct 2006
KO-Homology and Type I String Theory
R M G Reis, R J Szabo and A Valentino
Abstract
We study the classification of D-branes and Ramond-Ramond fields in
Type I string theory by developing a geometric description of
KO-homology, analogous to the Baum-Douglas construction. 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 a
certain geometric invariant which is used, along with a definition of
the real Chern character in KO-homology, to derive cohomological index
formulas in certain dimensions. 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 also naturally captures the
coupling of Ramond-Ramond fields to background D-branes which cancel
global anomalies in the string path integral. We argue that this is
related to a physical interpretation of bivariant KK-theory. We also
provide a construction of the holonomies of Ramond-Ramond fields in
terms of topological KO-chains.
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