The String Coffee Table

Sharpe on Derived Categories and Strings on Stacks

Posted by Urs Schreiber

Lots of things to talk about, but, unfortunately, I am busy. But I can quickly provide the following link.

Yesterday, at ESI, Eric Sharpe gave a talk

Eric Sharpe
Derived categories in physics
(slides available here).

(The slides are very pretty. Lots of animations usually spice them up, but these are lost in the above pdf.)

The first part reviews some aspects of the description of D-branes in terms of derived categories ($\to$, $\to$).

The second part is on the study of sigma-models whose targets are orbifolds (stacks) that are not global quotients ($\to$, $\to$).

The main point is that it seems to make sense to have strings propagating on orbifolds different from global quotients. Even though for target spaces that are, as stacks, gerbes (not to be confused with the structure incorporating the Kalb-Ramond field) there seems to be a failure of cluster decomposition, this is apparently simply due to the fact that these targets have to be regarded as disconnected.

This is discussed in the recent paper

S. Hellerman, A. Henriques, T. Pantev, E. Sharpe, M. Ando
Cluster decomposition, T-duality, and gerby CFT’s
hep-th/0606034.