How are Feynman graphs resumed by the Loop Vertex Expansion?

TL;DR

This paper clarifies the specific Feynman graphs resummed by the Loop Vertex Expansion and proposes a conjecture for the $$ theory in non-integer dimensions.

Contribution

It identifies the set of Feynman graphs summed in the Loop Vertex Expansion and introduces a conjecture for $$ theory in non-integer dimensions.

Findings

Clarification of Feynman graphs resummed by the Loop Vertex Expansion

Formulation of a conjecture for $$ theory in non-integer dimensions

Abstract

The purpose of this short letter is to clarify which set of pieces of Feynman graphs are resummed in a Loop Vertex Expansion, and to formulate a conjecture on the $\phi^4$ theory in non-integer dimension.