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In particle physics, supersymmetry (often abbreviated susy) is a symmetry that relates elementary particles of one spin to other particles that differ by half a unit of spin and are I am looking for resources that construct and justify the index notation given to the weyl spinors, especially van der waerden spinor notation. To be precise (i just saw this post), without really complicating the discussion
In simple words, there exists a group which commutes with the lorentz group and leaves the susy algebra (the anticommutators) invariant 2 i am currently trying to read into susy and i am running into trouble with the van der waerden spinor notation for weyl spinors The largest such group is referred to as r.
I think i figured out the meaning of this after some research so, i am posting an answer to my own question
The answer is there is nothing called $\mathcal {n}= (1,1)$ superalgebra The superalgebra is always named by $\mathcal {n}$ with integers The $\mathcal {n}= (1,1)$ actually means a supergravity multiplet so my original question was wrong We get this multiplet as the massless level of.
However, susy representations furnish reducible poincaré representations, so supermultiplets in general correspond to multiple particles having the same mass, which are related by supersymmetry transforms In this context, the broader term multiplet is used interchangeably with supermultiplet. If you spend some time looking in detail at the arguments that string theory requires supersymmetry, you'll find that they are not watertight (how could they be, since we still can't say/don't know precisely what string theory is?) basically, some string theorists argue that that the usual classification depends too strongly on choosing nearly trivial boundary conditions and backgrounds, and.
In strathdeee's extended poincare supersymmetry, the first entry on page 16 lists the massless multiplets of 6d $\\mathcal{n} = (1,0)$ supersymmetry as $2^2 = (2,1
4 supergravity by daniel z freedman and antoine van proeyen is quite excellent for illustrating clifford algebra techniques and calculations in the classical susy/sugra in general (in the component formalism) The book has several calculations illustrated and plenty of exercises.
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