Clifford Algebra for Quantum Field Theory, Supersymmetry, Supergravity

[shinobi20]

I'm currently trying to learn Clifford algebra or more specifically spinors, in higher dimensions. My goal is to study AdS/CFT, but an essential part of learning it is to understand SUSY which then needs some element of Clifford algebra in higher dimensions.

I have consulted,
Introduction to the AdS/CFT Correspondence by Horaƫiu Năstase
Supergravity by Daniel Z. Freedman and Antoine Van Proeyen

The book by Năstase only discussed it in a section and is extremely compact, no motivation and discussion of the steps. The book by Freedman devoted two sections and is more comprehensive than Năstase, but it is still lacking in motivation with the steps and some equations.

So, I'm looking for books or lectures more devoted to Clifford algebra/spinors in higher dimensions that is tailored specifically for people pursuing AdS/CFT or quantum field theory. I believe Clifford algebra/spinors in higher dimensions resources can be extremely varied in its presentation depending on the target audience. I've searched the web for some lectures but either it is also too brief and just a list of equations or it is geared towards mathematicians with theorem-proof format.

An example of the briefness and no motivation style is to just present the higher dimensional $\gamma$-matrices as a bunch of tensor products of $\sigma$-matrices. My question is, why? No explanation or motivation at all, this goes on throughout the books I listed above, just listing down and checking that every equation is consistent with the previous.

 

[stevex]

Start with David Hestenes spacetime algebra. Very good intro with intuition for physics.

 

[haushofer]

Zee's book on Group Theory has a nice overview on Clifford algebras.

 

[billtodd]

For susy there's no better than sueperspace and 1000 and 1 lessons by jim gates et al.