Abstract. In this paper we discuss some topics on the geometry of type II superstring backgrounds with D-branes, in particular on the geometrical meaning of the D-brane charge, the Ramond-Ramond fields and the Wess-Zumino action. We see that, depending on the behaviour of the D-brane on the four non-compact space-time directions, we need different notions of homology and cohomology to discuss the associated fields and charge: we give a mathematical definition of such notions and show their physical applications. We then discuss the problem of corretly defining Wess-Zumino action using the theory of p-gerbes. Finally, we recall the so-called *-problem and make some brief remarks about it.

Key words: D-branes; Differential and Algebraic Geometry

E-print number: 0909.0689
Cited: by
Refers: to

Received 7 September 2009, accepted for publication 20 October 2009
Published 4 November 2009