Appears in collection : Combinatorics and Arithmetic for Physics: special days 2023

Loop Vertex Expansion (LVE) was developed for the construction of QFT models with local and non-local interactions. Using LVE, one can prove the analyticity in the finite cardioid-like domain in the complex plain of the coupling constant of the free energies and cumulants of various vector, matrix, or tensor-type models. In this talk, applying the idea of choosing the initial approximation depending on the coupling constant, I construct the analytic continuation of the free energy of the quartic matrix model beyond the standard LVE cardioid.