Deflation

Vector two-point functions with exact deflation

$$\begin{align} C_{rr'}^{AB}(t) ~ = &~ \sum_{\vec{x},\vec{y}} \sum_{j=1}^K \sum_{l=1}^K \frac{1}{\lambda_j +i r\mu} \frac{1}{\lambda_l +i r' \mu'} \langle v_j(y) | \gamma_5 \Gamma_A | v_l(y)\rangle \; \langle v_l(x) | \gamma_5 \Gamma_B | v_j(x)\rangle + \nonumber \\ % & +\frac{1}{N} \sum_{\vec{x},\vec{y}}\sum_{\eta}\sum_{j=1}^K \frac{1}{\lambda_j +i r\mu} \langle v_j(y) | \gamma_5 \Gamma_A |\widetilde\phi_{r'}^{\eta_\alpha}(y)\rangle \; \langle \eta_\alpha(x) | \gamma_5 \Gamma_B |v_j(x)\rangle + \nonumber \\ % & +\frac{1}{N}\sum_{\vec{x},\vec{y}}\sum_\eta \sum_{j=1}^K \frac{1}{\lambda_j +i r'\mu'}\langle v_j(x) | \gamma_5 \Gamma_B |\eta_\beta(x) \rangle \; \langle \widetilde\phi_{-r}^{\eta_\beta}(y) | \gamma_5 \Gamma_A |v_j(y)\rangle + \nonumber \\ % & +\frac{1}{N} \sum_{\vec{y}} \sum_\eta \langle \widetilde\phi_{-r}^{\eta_\beta}(y) | \gamma_5 \Gamma_A |\widetilde\phi_{r'}^{\eta_\alpha}(y)\rangle (\gamma_5 \Gamma_B)_{\alpha\beta} \; , \label{Cfin} \end{align}$$

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