UV/IR connection, a matrix perspective

TL;DR

This paper demonstrates that the matrix formulation of non-commutative field theories reveals the IR/UV mixing phenomenon transparently by connecting non-local interactions to diagram non-planarity, clarifying long-range effects.

Contribution

It establishes an equivalence between matrix and mixed space formulations, providing new insights into IR/UV mixing in non-commutative field theories.

Findings

IR/UV mixing is linked to non-planar diagrams.

Matrix formulation makes non-locality and IR divergences transparent.

Clarifies the relation between long-range effects and diagram topology.

Abstract

We show that the matrix formulation of non-commutative field theories is equivalent, in the continuum, to a formulation in a mixed configuration-momentum space. In this formulation, the non-locality of the interactions, that leads to the IR/UV mixing, becomes transparent. We clarify the relation between long range effects (and IR divergences) and the non-planarity of the corresponding Feynman diagrams.