Paramagnetic dominance, the sign of the beta function and UV/IR mixing in non-commutative U(1)

TL;DR

This paper analyzes non-commutative U(1) gauge theory, demonstrating how paramagnetic effects dominate over diamagnetic effects, leading to a negative beta function and explicit UV/IR mixing at one loop.

Contribution

It provides the first explicit calculation showing paramagnetic dominance causes the negative beta function and UV/IR mixing in non-commutative U(1) gauge theory.

Findings

Negative beta function results from paramagnetism causing UV anti-screening.

Explicit one-loop calculations of divergences in two, three, four-point functions.

UV/IR mixing leads to IR renormalization of the coupling constant.

Abstract

U(1) gauge theory on non-commutative Minkowski space-time in the Feynman-'t Hooft background gauge is studied. In particular, UV divergences and non-commutative IR divergent contributions to the two, three and four-point functions are explicitly computed at one loop. We show that the negative sign of the beta function results from paramagnetism --producing UV charge anti-screening-- prevailing over diamagnetism --giving rise toUV charge screening. This dominance in the field theory setting corresponds to tachyon magnification dominance in the string theory framework. Our calculations provide an explicit realization of UV/IR mixing and lead to an IR renormalization of the coupling constant, where now paramagnetic contributions produce screening and diamagnetic contributions anti-screening.