Finite Temperature effects on the Induced Chern-Simons term in noncommutative geometry

TL;DR

This paper investigates how finite temperature influences the induced Chern-Simons term in three-dimensional noncommutative spaces, revealing UV/IR mixing and a Fermi-Bose transmutation at high temperatures.

Contribution

It provides the first detailed analysis of finite temperature effects on the induced Chern-Simons term in noncommutative geometry, including UV/IR mixing and high-temperature behavior.

Findings

Confirmed zero-temperature parity odd result

Identified UV/IR mixing in the even parity part

Discovered Fermi-Bose transmutation at high temperature

Abstract

The one-loop contribution to vacuum polarization is calculated for the adjoint fermions in three dimensional noncommutative spaces, both at zero and finite temperature. At zero temperature, we confirm a previously found result for the parity odd part and subsequently analyze the even parity part, which exhibits UV/IR mixing. We discuss in detail, two regimes of the high temperature behavior of the parity odd part. When the thermal wavelength is much smaller, as compared to the noncommutativity scale, we find an interesting Fermi-Bose transmutation in the nonplanar part.