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Is there any easy way to compute the OPE of graviton vertex operators?

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I would like to know if there is any easy way to perform the operator product expansion of the following

$:\partial X^{\mu}\bar{\partial}X^{\nu}e^{ik_{\rho}X^{\rho}}(z,\bar{z})::\partial X^{\alpha}\bar{\partial}X^{\beta}e^{ik_{\sigma}X^{\sigma}}(w,\bar{w}):$

I tried to find all the contraction terms and use wick's theorem, but it turns out to be a mission impossible. How to compute it quickly?

asked Feb 23, 2017 in Theoretical Physics by XIaoyiJing (50 points) [ no revision ]
recategorized Feb 23, 2017 by XIaoyiJing

Check the 2nd chapter of Polchinski. All the necessary techniques are given there.

commented Feb 24, 2017 by Andrey Feldman (904 points) [ revision history ]
edited Feb 24, 2017 by Andrey Feldman

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