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

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)?

• 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. – Rexcirus May 1 '15 at 21:33