Topics on the geometry of D-brane charges and Ramond-Ramond fields

TL;DR

This paper explores the geometric structures underlying D-brane charges and Ramond-Ramond fields in type II superstring backgrounds, proposing mathematical frameworks to better understand their physical implications.

Contribution

It introduces new geometric and homological notions tailored for D-brane charges and Ramond-Ramond fields, and applies p-gerbe theory to define the Wess-Zumino action.

Findings

Different homology and cohomology notions are needed based on D-brane behavior.

Mathematical definitions of these notions are provided with physical applications.

The p-gerbe theory offers a consistent way to define the Wess-Zumino action.

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.