Primer on conformal / dual conformal symmetry

[earth2]

Hey guys,

i am looking for some primer on conformal, dual conformal symmetry, respectively. I have to read a lot of stuff about scattering amplitudes for uni and in recent papers people talk a lot about these symmetries... unfortunately i am not so familiar with them, so does any of you know a good reference for studying them (lecture notes or whatever)?

Thanks!
earth2

 

[haushofer]

For conformal theories you could consult the text of DiFrancesco et. al. It's the standard work on the subject and doesn't need a lot of prerequisites.

 

[chrispb]

There are a plethora of papers on the subject. Some of the first few that helped me out were Drummond's (http://arxiv.org/abs/0807.1095) and Berkovits and Maldacena's (http://arxiv.org/abs/0807.3196). Generally, all of the papers by Drummond in the past few years have been about this topic (http://arxiv.org/find/hep-th/1/au:+Drummond_J/0/1/0/all/0/1). Maldacena has been involved in this game from the AdS/CFT side, exploring the connection between amplitudes and Wilson loops, which involves the connection between the conformal and dual conformal groups. Arkani-Hamed et al have been studying N=4 SYM for the past two or so years, and have written down a formula for tree amplitudes as integrals over a geometric structure known as the Grassmannian that is manifestly Yangian-invariant. Drummond talks at length about the Yangian in some of his papers; the basic idea is if something is invariant under the superconformal AND dual superconformal algebras, it must be invariant under a full (infinite-dimensional) algebra known as the Yangian of the superconformal algebra.

If you want to get a more physical understanding of the presence of the dual conformal symmetry in physics, I'd suggest you start by learning about the amplitudes/Wilson loop connection.

 

[negru]

You'll eventually also want to study momentum twistors since they're very useful for all of this.
http://arxiv.org/abs/0909.0250

That's not a particularly easy paper to follow, you might find some better ones. There's plenty of papers on these things, your best bet is to just look through as many as you can and see which you like best.

I was actually just looking through this PhD thesis of Henn's, maybe it's useful
http://arxiv.org/abs/0903.0522

 

[chrispb]

How could I forget about Mason and Skinner? Sigh.

As far as twistors themselves go, Witten gives a decent introduction to them in (http://arxiv.org/abs/hep-th/0312171). In my opinion, M&S gives a pretty decent introduction to momentum twistors.

 

[earth2]

Alright, thank you all! Now i have plenty to read :)