Why must N=2 SUSY compactifications use Kähler manifolds?

[GoldPheonix]

In this paper*, Brian Greene just asserts that:

"In order to contribute nine to the central charge, the dimension of M must be six, and to ensure the additional condition of N = 2 supersymmetry, M must be a complex Kahler manifold."

Is there some paper that discusses the relationship between Kahler geometry and N=2 SUSY? This assertion does not seem trivial, although I'm not very well-versed in string theory or SUSY.



*http://arxiv.org/PS_cache/hep-th/pdf/9702/9702155v1.pdf (Page 9, 2nd paragraph)

 

[negru]

Ok arxiv isn't working now, but you should try the paper "Chiral Rings in N=2 Superconformal Theories", by Vafa and some friends. Unless I'm mistaken there should be some details there.

Otherwise Brian Greene should have another paper based on that one, maybe called "calabi yau manifolds", or something with geometry in it, I think around 1998 or so. Pretty sure that has more details.

 

[negru]

Oops actually I think the Greene paper I'm talking about is the one you've mentioned :D

arxiv's fault, can't check anything. For some reason I assumed you were talking about Greene's new paper

 

[MTd2]

Ok arxiv isn't working now

For now, just change the initial part of the url for xxx.lanl.gov, or some other mirror server.

 

[crackjack]

Ch15 of Green, Schwarz, Witten should have something on this.

 

[negru]

This old school one could also be useful:
"Supersymmetry and Kahler Manifolds", by Zumino.
http://ccdb4fs.kek.jp/cgi-bin/img_index?7909068