The \beta-function in duality-covariant noncommutative \phi^4-theory

TL;DR

This paper calculates the one-loop eta-functions for a four-dimensional duality-covariant noncommutative -theory, showing renormalisability and behavior of the coupling and frequency parameters at specific limits.

Contribution

It provides the first one-loop eta-function calculations for the duality-covariant noncommutative -theory, demonstrating its renormalisability and the behavior of parameters at key limits.

Findings

-theory is renormalisable to all orders.

eta_ and eta_functions are non-negative at one-loop.

eta_ and eta_ vanish at =1 and =0 limits.

Abstract

We compute the one-loop \beta-functions describing the renormalisation of the coupling constant \lambda and the frequency parameter \Omega for the real four-dimensional duality-covariant noncommutative \phi^4-model, which is renormalisable to all orders. The contribution from the one-loop four-point function is reduced by the one-loop wavefunction renormalisation, but the \beta_\lambda-function remains non-negative. Both \beta_\lambda and \beta_\Omega vanish at the one-loop level for the duality-invariant model characterised by \Omega=1. Moreover, \beta_\Omega also vanishes in the limit \Omega \to 0, which defines the standard noncommutative \phi^4-quantum field theory. Thus, the limit \Omega \to 0 exists at least at the one-loop level.