The two point function of an operator dual to a scalar field in ADS/CFT can obtained directly from computation of the on-shell action in momentum space and then taking it back to position space. The procedure is shown in many papers and it is a common point to say that the only non-trivial contribution comes from non-polynomial terms in the momentum, and everyone arrives at the following integral (up to constants): \begin{equation} \langle\mathcal{O}(\bar{x}_1)\mathcal{O}(\bar{y}_1)\rangle=\int\frac{\mathrm{d}^4\bar{p_1}}{(2\pi)^4}|p_1|^{2\nu}\log(|p_1|\epsilon)e^{-i\bar{p}_1(\bar{x}_1-\bar{y}_1)} \end{equation} and suddenly the result of the two point function. My question is: How can this integral can be done?


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