Is anyone else working through this paper: A theory of generalized Donaldson-Thomas invariants, by Dominic Joyce, Yinan Song? I am trying to verifying example 6.2 (m=2 for simplicity) using only the definitions, namely:
J^{2\alpha}(\tau) = -1/4$$J^{2\alpha}(\tau) = -1/4,$$
(where \alpha$\alpha$ satisfies M^{\alpha}_ss = M^{\alpha}_st$M^{\alpha}_{\mathrm{ss}} = M^{\alpha}_{\mathrm{st}}$ and that Ext^1(E, E)=0$\mathrm{Ext}^1(E, E)=0$ for any E \in M^{\alpha}_ss$E \in M^{\alpha}_{\mathrm{ss}}$ and finally that the only object of M^{m\alpha}_ss$M^{m\alpha}_{\mathrm{ss}}$ is E ^{\oplus m}$E ^{\oplus m}$).
I keep getting -3/4. Has anyone else attempted to make such a computation? Did you get the answer you are supposed to get?
