A Symplectic Majorana Spinors in 5 Dimension

[Francisca Ramirez]

I need to know if the Symplectic Majorana spinors in 5 dimension have any advantage with respect to the Dirac spinors in 5 dimension, since they have the same number of components. For example if the Symplectic Majorana spinors have a manifested symmetry that the Dirac spinors don't have, or if it's more easy to work with the Symplectic Majorana spinors.

 

[haushofer]

Have you checked

http://arxiv.org/abs/hep-th/9910030

?

 

[Francisca Ramirez]

No, i have not see it. I am going to check it.
Thank you!

 

[haushofer]

Well, just a small hint: they got their name from a certain symm. property :P

Especially in supergravity, where chirality often is not that important, we like Majorana spinors. In 2,3 and 4 dimensions we can define them, but in 5 dimensions we can't. But we can go the the next best thing: symplectic Majorana. Van Proeyen explains how and why.

 

[mitchell porter]

Tomas Ortin, in appendix D of "Gravity and Strings" (SECOND edition), says

There are no Majorana representations in d = 5, but only pairs of (complex) symplectic-Majorana spinors that can be combined into a single unconstrained Dirac spinor. Doing this, however, hides this structure and makes it more difficult (or impossible) to construct five-dimensional supergravities with the most general couplings. We will show how to deal with these spinors...

but in Australia, Google's preview is limited and doesn't let me see the actual argument.

 

[Francisca Ramirez]

Thank you very mach!