$\lambda \phi^4$ Theory I: The Symmetric Phase Beyond NNNNNNNNLO

TL;DR

This paper extends perturbative calculations of 2D $bbb4$ theory to high order, demonstrating how resummation techniques recover strong coupling behavior and accurately determine critical properties matching known results.

Contribution

It provides the first high-order perturbative expansion up to N$^8$LO for the 2D $bbb4$ theory in the symmetric phase, and shows how to extract critical properties using resummation.

Findings

Perturbative expansion extended up to N$^8$LO.

Resummation techniques successfully recover strong coupling behavior.

Critical properties match known exact results.

Abstract

Perturbation theory of a large class of scalar field theories in $d<4$ can be shown to be Borel resummable using arguments based on Lefschetz thimbles. As an example we study in detail the $\lambda \phi^4$ theory in two dimensions in the $Z_2$ symmetric phase. We extend the results for the perturbative expansion of several quantities up to N$^8$LO and show how the behavior of the theory at strong coupling can be recovered successfully using known resummation techniques. In particular, we compute the vacuum energy and the mass gap for values of the coupling up to the critical point, where the theory becomes gapless and lies in the same universality class of the 2d Ising model. Several properties of the critical point are determined and agree with known exact expressions. The results are in very good agreement (and with comparable precision) with those obtained by other non-perturbative approaches, such as lattice simulations and Hamiltonian truncation methods.