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.fzero said: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.
It lists the algebra but again without derivation of how supercharges mix, though it's nice that de-Sitter superalgebra is also listed.Thomas Larsson said:http://arxiv.org/abs/hep-th/0108200" , perhaps. Page 65 looks promising.
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.Haelfix said:Try this:
arXiv:hep-th/0406154v6
The superconformal algebra in 4D is a mathematical framework that describes the symmetries and transformations of a superconformal field theory in four dimensions. It is a combination of the conformal algebra, which describes the symmetries of a conformal field theory, and the supersymmetry algebra, which introduces extra degrees of freedom to the theory.
The superconformal algebra is important because it allows us to study and understand the properties of superconformal field theories, which are important in theoretical physics and have applications in areas such as string theory and condensed matter physics. It also provides a powerful tool for solving and analyzing these complex theories.
There are many resources available for learning about the superconformal algebra in 4D. Some recommended sources include textbooks on theoretical physics and field theory, scientific articles and papers on the topic, and online lectures and courses offered by universities or organizations related to physics.
Some key concepts related to the superconformal algebra in 4D include conformal symmetry, supersymmetry, central charges, and the structure of the algebra itself. It is also important to understand how these concepts are applied in different contexts, such as in string theory or in the study of black holes.
Yes, there are ongoing developments and open questions surrounding the superconformal algebra in 4D. Some current areas of research include the study of the algebra in different dimensions, the search for new superconformal field theories, and the application of the algebra to other areas of physics such as holography and quantum gravity. There are also unanswered questions about the algebra's role in understanding the fundamental nature of the universe and its connections to other areas of physics.