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

TL;DR

This paper reviews Borel summability in quantum field theory, demonstrating a proof for the $ ext{phi}^4_4$ planar model using multiscale analysis, with implications for broader applications in condensed matter and field theory.

Contribution

It presents a multiscale analysis approach to establish Borel summability of the $ ext{phi}^4_4$ planar theory, extending techniques to future complex models.

Findings

Proof of Borel summability for $ ext{phi}^4_4$ planar theory

Effective multiscale analysis techniques demonstrated

Potential for applying methods to other models

Abstract

We review the issue of Borel summability in the framework of multiscale analysis and renormalization group, by discussing a proof of Borel summability of 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 that we use have already been proved effective in the analysis of various models of consended matter and field theory; therefore, we take the $\phi^{4}_4$ planar theory as a toy model for future applications.