Corrected loop vertex expansion for Φ24 theory

Abstract

This paper is an extended erratum to Rivasseau and Wang [J. Math. Phys. 53, 042302 (2012); e-print arXiv:1104.3443 [math-ph]], in which the classic construction and Borel summability of the ϕ24 Euclidean quantum field theory was revisited combining a multi-scale analysis with the constructive method called Loop Vertex Expansion (LVE). Unfortunately we discovered an important error in the method of Rivasseau and Wang [J. Math. Phys. 53, 042302 (2012); e-print arXiv:1104.3443 [math-ph]]. We explain the mistake, and provide a new, correct construction of the ϕ24 theory according to the LVE.