Where can I read about the superconformal algebra in 4D?

[petergreat]

I know both the 4D SUSY algebra and conformal algebra. However, I'm struggling to find elementary introductions to the 4D superconformal algebra. Anyone has suggestions? Neither introductory SUSY books (e.g. Wess & Bagger) nor CFT books (like Di Francesco) seem to cover this...

 

[petergreat]

BTW superstring books cover the 2D case which is simply the super-Virasoro algebra, but I'm looking for the 4D case.

 

[fzero]

There are no elementary introductions that I'm aware of. http://arxiv.org/abs/hep-th/9712074 will not be the easiest read, but it's probably one of the few places where details of the representation theory are given.

 

[petergreat]

Thanks! I'll have a look.

 

[samalkhaiat]

M. F. Sohnius, Introducing supersymmetry, Phys. Rep. 128, 39, 1985.
E.S. Fradkin and A.A. Tseytlin, Conformal supergravity, Phys. Rep. 119, 233, 1985.

I would encourage you to apply the general methods described in the thread;

www.physicsforums.com/showthread.php?t=172461

to the following group element

$$g = \exp \left[i \left(\alpha D + a_{a}P^{a} - (1/2) \omega_{ab} J^{ab} + c_{a}K^{a} + \epsilon Q + \bar{\epsilon} \bar{Q} \right)\right]$$

Hint: use the fact that for every superconformal transformation S, the mapping RSR (where R is superinversion) is superconformal. For example you can take S to be super Poincare' or super scale, to obtain a new superconformal transformation.

regards

sam

 

[Thomas Larsson]

http://arxiv.org/abs/hep-th/0108200" , perhaps. Page 65 looks promising.

 

[Haelfix]

Try this:

arXiv:hep-th/0406154v6

 

[petergreat]

There are no elementary introductions that I'm aware of. http://arxiv.org/abs/hep-th/9712074 will not be the easiest read, but it's probably one of the few places where details of the representation theory are given.

I had a look. It's nice that the paper explains in detail how to embed the (d-1,1) spinor supercharge Q into the (d,2) spinor supercharges Q and S. However, I'm unsatisfied with the fact that when the algebra is finally written down on page 17 and 18, the anti-commutation relations between the supercharges are stated without proof. The author says it's just a straight forward exercise of using Jacobi identities to deduce them, but it seems daunting to me... Maybe I'll try when I have time.

http://arxiv.org/abs/hep-th/0108200" , perhaps. Page 65 looks promising.

It lists the algebra but again without derivation of how supercharges mix, though it's nice that de-Sitter superalgebra is also listed.

Try this:
arXiv:hep-th/0406154v6

I know too little about supergroups to read this, but it seems that once I can understand this, deriving the algebra will be an easy task for me.

 

[haushofer]

Try the lecture notes of Van Proeyen about SUGRA (e.g. A Menu of Supergravities), there the whole (super)conformal tensor calculus is treated explicitly.