Open string amplitude with higher vertices

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In Polchinski's String Theory, section 6.2, the tree level amplitude for open strings with higher vertices are given (6.2.18-20).

The amplitude

$\langle \prod_i[e^{ik_i\cdot X(z_i,\bar {z_i})}]_r\prod_j\partial X^{\mu_j}(z_j')\prod_k\bar \partial X^{\nu_k}(\bar z_k'')\rangle$

yields result

$\text{other terms }\times \langle\prod_j[v^{\mu_j}+q^{\mu_j}]\prod_k[\tilde v^{\mu_k}+\tilde q^{\mu_k}]\rangle$

However I could not repeat the calculation there. To be specific, I don't know what source term $J$ corresponds to the $\partial X^\mu$ terms in the amplitude. Could you help me with this or point out some notes with more detailed calculation?

asked Apr 21, 2014
edited Apr 21, 2014

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