quantum field theory - The superconformal algebra

1. 
   

   How does one derive the superconformal algebra?

   
   


2. 
   

   Especialy how to argue the existence of the operator $S$ which doesn't exist either in either the supersymmetric algebra or the conformal algebra?

   
   



3. 
   

   What is the explanation of the convention of choosing If $J _ \alpha ^\beta$ as a generator of $SU(2) \times SU(2)$ and $R^A _B$ and $r$ are the generators of the $U(m)$ R-symmetry ( $m \neq 4$)? How does one get these $R$ and $r$?

   
   


4. 
   

   One further defines $R_1, R_2$ and $R_3$ as the generators of the Cartan subalgebra of $SU(4)$ (the $N=4$ R-symmetry group) where these are defined such that $R_k$ has $1$ on the $k^{th}$ diagonal entry and $-1$ on the $(k+1)^{th}$ diagonal entry.

   
   

Using the above notation apparently one of the $Q-S$ commutation looks like,

$\{ S^A_\alpha , Q^\beta _B\} = \delta ^A_B J^\beta _\alpha + \delta ^\beta _\alpha R^A_B + \delta ^A_B \delta ^\beta _\alpha (\frac{H}{2} + r \frac{4-m}{4m})$

I would like to know how the above comes about and why the above equation implies the following equation (..each of whose sides is defined as $\Delta$)

$2\{ Q_4 ^- , S^4_ - \} = H - 3J_3 + 2\sum _{k=1} ^ 3 \frac{k}{4} R_k$

I can't understand how to get the second of the above equations from the first of the above and why is this $\Delta$ an important quantity.

{Is there any open source online reference available which explains the above issues?