# Vanishing correlation function

Mirror Symmetry p. 206, Eq. 10.192.

I have an operator $$\mathcal{O}$$ that commutes with my supercharge $$\overline{Q}_+$$, $$\left[\overline{Q}_+, \mathcal{O} \right]=0$$. Why does the correlation function vanish? $$\left< \{\overline{Q}_+, \psi^i\} \mathcal{O} \right> = 0\tag{10.192}$$ Where $$\psi^i$$ is a fermionic variable and $$\langle \mathcal{O}(\tau_1) \dots \mathcal{O}(\tau_s) \rangle = \int \mathcal{D}z \mathcal{D}{\psi} \mathcal{D}{\overline{\psi}} \vert_P e^{-S(z, \psi, \overline{\psi})} \mathcal{O}(\tau_1) \dots \mathcal{O}(\tau_s).\tag{10.190}$$

Eq. (10.192) follows because the supercharge $$\overline{Q}_+$$
• supercommutes with the operator $${\cal O}$$;