# Different chirality in IIB (N=2, D=10) supergravity

In some papers on type IIB supergravity (N=2, D=10) the dilatino is taken to be of positive chirality. In some other papers dilatino is choosen instead of negative chirality.

Is it possible to map one convention to the other? What is the standard method?

I think I can give you some hints to help you spot where the whole thing starts, though I do not know if this is something I am allowed to do (I mean not give a definite answer but rather some logical steps).

In any case.

In order to go from one convention to the other, you need to figure out what is going on.

Also, it would be a good thing to check that there is no typo in the paper. It is a common situation. One makes a typo and then they derive some important results, and in subsequent papers other authors carry the typo as they didn't check. It has happened before, it will happen again.

What do we know about type $IIB$ in $10d$?

It is a maximal supergravity in ten dimensions which cannot be (directly) obtained from d = 11. It contains 32 real supercharges in two Majorana-Weyl spinors of the SAME chirality.

$\Gamma$-matrices

They are unique (up to a similarity transformation) in even dimensions; for odd dimensions, there are two inequivalent representations.

For d=10,

$$\Gamma_{chiral} = \Gamma_0 \cdots \Gamma_9$$

and there is no other way to write it down, see i.e Polchinski vol 2, appendix.

So, it seems we can narrow down the confusion.

The $\gamma$-matrices are not causing -or better yet should not be causing- this chirality change. Now, it seems, that the change in chirality should be in the spinors. What I mean is that the left-chiral of one paper is the right-chiral of the other. At least this is what sounds reasonable in my head.

This might have to do with the conventions that each author is using.

And it makes sense, since there is no universal way of writing down SUSY. The conventions are very different from one paper to the other, so it has to do with how they write down the chiral supermultiplets.

Is there a consistent way to do it? If I am correct in my above considerations, then by knowing both of the SUSY conventions that they used, you'll be able to figure out where they have a relative minus change or something like that.

I know that this does not answer fully your question, but I sincerely hope I helped. At least a bit. If not, apologies.

Cheers