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We review the issue of Borel summability in the framework of multiscaleanalysis and renormalization group, by discussing a proof of Borel summabilityof the $\phi^{4}_4$ massive euclidean planar theory; this result is not new,since it was obtained by Rivasseau and 't Hooft. However, the techniques thatwe use have already been proved effective in the analysis of various models ofconsended matter and field theory; therefore, we take the $\phi^{4}_4$ planartheory as a toy model for future applications.

Borel summability of $\phi^{4}_{4}$ planar theory via multiscale analysis