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While bare diagrammatic series are merely Taylor expansions in powers ofinteraction strength, dressed diagrammatic series, built on fully or partiallydressed lines and vertices, are usually constructed by reordering the barediagrams, which is an a priori unjustified manipulation, and can even lead toconvergence to an unphysical result [Kozik, Ferrero and Georges, PRL 114,156402 (2015)]. Here we show that for a broad class of partially dresseddiagrammatic schemes, there exists an action $S^{(\xi)}$ depending analyticallyon an auxiliary complex parameter $\xi$, such that the Taylor expansion in$\xi$ of correlation functions reproduces the original diagrammatic series. Theresulting applicability conditions are similar to the bare case. For fullydressed skeleton diagrammatics, analyticity of $S^{(\xi)}$ is not granted, andwe formulate a sufficient condition for converging to the correct result.

Shifted-Action Expansion and Applicability of Dressed Diagrammatic Schemes