Dynamics of O(N) Model in a Strong Magnetic Background Field as a Modified Noncommutative Field Theory

TL;DR

This paper derives an effective scalar field theory in a strong magnetic background, showing it resembles noncommutative field theory but without UV/IR mixing, using worldline formalism and Landau level analysis.

Contribution

It introduces a modified noncommutative field theory derived from an O(N) model in strong magnetic fields, highlighting the absence of UV/IR mixing.

Findings

Effective action matches noncommutative field theory in strong magnetic limit

UV/IR mixing is absent in the modified theory

Results obtained via worldline formalism and Landau level dominance

Abstract

In the presence of a strong magnetic field, the effective action of a composite scalar field in an scalar O(N) model is derived using two different methods. First, in the framework of worldline formalism, the 1PI n-point vertex function for the composites is determined in the limit of strong magnetic field. Then, the n-point effective action of the composites is calculated in the regime of lowest Landau level dominance. It is shown that in the limit of strong magnetic field, the results coincide and an effective field theory arises which is comparable with the conventional noncommutative field theory. In contrast to the ordinary case, however, the UV/IR mixing is absent in this modified noncommutative field theory.