What is the significance of self-duality and anti self-duality in supergravity?

Question

So I see the terms "self-dual" and "anti self-dual" appear routinely in supergravity/string thery, e.g. the fact that Type IIB supergravity contains a real self-dual rank-5 antisymmetric tensor $F_{\hat{\mu}_1, \ldots, \hat{\mu}_5}$ (hats denote 10 dimensional indices). I have also read that these things are important in studying Type IIB supergravity on $S^5$.

1. What is the physical implication of self-duality, or anti-self-duality?

2. What is the connection to group theory (where sometimes you have to include a factor of 1/2 in counting the dimensions of irreducible representations in the Young Tableaux, when you encounter self-dual or anti-self dual tensors)?

This post imported from StackExchange Physics at 2015-05-10 11:27 (UTC), posted by SE-user leastaction

Comments

Check p.78 of Supergravity (Van Proeyen, Freedman). Keep in mind that the self dual condition implies that the independent components of the tensor are divided by two.

This post imported from StackExchange Physics at 2015-05-10 11:27 (UTC), posted by SE-user Rexcirus