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- Title
KO-HOMOLOGY AND TYPE I STRING THEORY.
- Authors
REIS, RUI M. G.; SZABO, RICHARD J.; VALENTINO, ALESSANDRO
- 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. 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 Cℓn-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.
- Subjects
D-branes; ISOMORPHISM (Mathematics); CHARACTERISTIC classes; STRING models (Physics); HOMOLOGY theory; ALGEBRAIC topology
- Publication
Reviews in Mathematical Physics, 2009, Vol 21, Issue 9, p1091
- ISSN
0129-055X
- Publication type
Article
- DOI
10.1142/S0129055X09003839