# A Question about Wall crossing formula

1. Nov 18, 2017

### kdv

I am looking at the wall-crossing formula for N=2 D=4 supersymmetry The Donaldson-Thomas "invariant" is supposedly given by

$$\Omega = -\frac{1}{2} Tr (-1)^{(2J_3)} (2J_3)^2$$
+
I don't understand how to use this formula. (By the way, the normalization is probably not the same for everyone so you may have seen something slightly different). Then my reference says that for the W bosons with charge $(0,\pm 2)$, we have $\Omega =-2$ in this normalization. This works if we set $J_3=1$ in the above formula. So I thought that maybe $J_3$ referred to the spin or helicity.

But then they say that for the dyons with charge $(\mp 1, \pm 2n )$, we have $\Omega= 1$. Now I don't see how to get this from the formula. I mean, I see that if I consider that there are two states with $J_3=1/2$ I get the answer but I don't understand why this should be correct.

Can someone help?

Last edited: Nov 18, 2017
2. Nov 23, 2017

### PF_Help_Bot

Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.