Non-commutative correspondences, duality and D-branes in bivariant K-theory. (English) Zbl 1166.81032

Brodzki, Jacek; Mathai, Varghese; Rosenberg, Jonathan; Szabo, Richard J.

Adv. Theor. Math. Phys. 13, No. 2, 497-552 (2009).

Summary: We describe a categorical framework for the classification of D-branes on noncommutative spaces using techniques from bivariant K-theory of \(C^*\)-algebras. We present a new description of bivariant K-theory in terms of noncommutative correspondences which is nicely adapted to the study of T-duality in open string theory. We systematically use the diagram calculus for bivariant K-theory as detailed in our previous paper [J. Brodzki, V. Mathai, J. Rosenberg and R. J. Szabo, Commun. Math. Phys. 277, No. 3, 643–706 (2008; Zbl 1162.58008)]. We explicitly work out our theory for a number of examples of noncommutative manifolds.

MSC:

81T30	String and superstring theories; other extended objects (e.g., branes) in quantum field theory
83E30	String and superstring theories in gravitational theory
81R60	Noncommutative geometry in quantum theory
81T75	Noncommutative geometry methods in quantum field theory

Citations:

Zbl 1162.58008