Existence of new nonlocal field theory on noncommutative space and spiral flow in renormalization group analysis of matrix models

TL;DR

This paper extends matrix model renormalization group analysis to include nonlocal antipodal interactions on fuzzy spheres, revealing fixed points and contrasting behaviors with noncommutative planes related to UV/IR mixing.

Contribution

It formulates RG equations with nonlocal antipodal interactions on fuzzy spheres and identifies nontrivial fixed points, advancing understanding of noncommutative field theories.

Findings

Identified several nontrivial fixed points in the fuzzy sphere limit.

Calculated scaling dimensions at these fixed points.

Found no consistent fixed points in the noncommutative plane limit.

Abstract

In the previous study, we formulate a matrix model renormalization group based on the fuzzy spherical harmonics with which a notion of high/low energy can be attributed to matrix elements, and show that it exhibits locality and various similarity to the usual Wilsonian renormalization group of quantum field theory. In this work, we continue the renormalization group analysis of a matrix model with emphasis on nonlocal interactions where the fields on antipodal points are coupled. They are indeed generated in the renormalization group procedure and are tightly related to the noncommutative nature of the geometry. We aim at formulating renormalization group equations including such nonlocal interactions and finding existence of nontrivial field theory with antipodal interactions on the fuzzy sphere. We find several nontrivial fixed points and calculate the scaling dimensions associated with them. We also consider the noncommutative plane limit and then no consistent fixed point is found. This contrast between the fuzzy sphere limit and the noncommutative plane limit would be manifestation in our formalism of the claim given by Chu, Madore and Steinacker that the former does not have UV/IR mixing, while the latter does.