Leading singularities in effective Kähler superpotential for general chiral N=1 superfield model

Using the Bogoliubov–Parasiuk theorem and the BPHZ renormalization procedure, we derive differential equations that sum the leading ultraviolet divergences of the Kähler potential in a general N=1 supersymmetric chiral theory with an arbitrary Kähler potential and chiral superpotential. Our approach recovers the known renormalizable Wess–Zumino limit and naturally extends to non‑renormalizable chiral interactions. The resulting equations are formulated covariantly in terms of the resummed Kähler metric and its associated curvature, allowing a systematic treatment of leading poles and leading logarithms. In some cases, the equations simplify drastically and can be analyzed in detail. For the Wess–Zumino model with a power‑like superpotential, the partial differential equation reduces to a nonlinear ordinary differential equation exhibiting scale invariance, critical behavior, and, for certain exponents, log‑periodic solutions for some types of chiral superpotentials. We also analyze a string-inspired no‑scale model with constant negative curvature and a massive quadratic superpotential, showing that the same reduction to an ODE occurs. In all cases, solutions display universal power–law scaling at large parameters. The obtained equations provide a practical tool to sum quantum corrections to the effective Kähler potential in string‑inspired inflationary models, where loop corrections often play a crucial role. We also extract the leading-log behavior of the effective potential in some supersymmetric models.