On space-time noncommutative theories at finite temperature

TL;DR

This paper investigates the renormalization and high temperature behavior of space-time noncommutative  theory using zeta function regularization, finding no mixed contributions and exploring formalism equivalences.

Contribution

It provides a detailed analysis of renormalization and high temperature expansion in noncommutative  theory, highlighting the absence of mixed contributions and formalism equivalences.

Findings

No mixed (non-planar) contributions to counterterms.

High temperature asymptotics lack mixed contributions.

Formalism equivalence between real and imaginary time under certain assumptions.

Abstract

We analyze renormalization and the high temperature expansion of the one-loop effective action of the space-time noncommutative \phi^4 theory by using the zeta function regularization in the imaginary time formalism (i.e., on S^1 x R^3). Interestingly enough, there are no mixed (non-planar) contributions to the counterterms as well as to the power-law high temperature asymptotics. We also study the Wick rotation and formulate assumptions under which the real and imaginary time formalisms are equivalent.