D-branes, Discrete Torsion and the McKay Correspondence

TL;DR

This paper investigates D-branes in type IIB string theory on orbifolds with discrete torsion, analyzing their moduli space, stringy homology, and the relation to the McKay correspondence, revealing nuanced differences between torsion concepts.

Contribution

It provides new insights into the moduli space of D-branes, the role of discrete torsion, and the connection between stringy homology and K-theory in orbifold backgrounds.

Findings

Discrete torsion affects the structure of D-branes and their moduli space.

Stringy homology and torsion are closely related but not equivalent.

Questions the duality between D-1 branes and fundamental strings.

Abstract

We analyze the D-branes of a type IIB string theory on an orbifold singularity including the possibility of discrete torsion following the work of Douglas et al. First we prove some general results about the moduli space of a point associated to the "regular representation" of the orbifold group. This includes some analysis of the "wrapped branes" which necessarily appear when the orbifold singularity is not isolated. Next we analyze the stringy homology of the orbifold using the McKay correspondence and the relationship between K-theory and homology. We find that discrete torsion and torsion in this stringy homology are closely-related concepts but that they differ in general. Lastly we question to what extent the D-1 brane may be thought of as being dual to a string.