Nonlocal regularisation of noncommutative field theories

TL;DR

This paper introduces a Poincaré-invariant nonlocal regularisation scheme for noncommutative field theories, analyzing one-loop corrections and discussing implications for UV-IR mixing and phenomenology.

Contribution

It presents a novel regularisation method that preserves Poincaré invariance and avoids UV-IR mixing issues in noncommutative field theories.

Findings

Regularisation scheme effectively manages nonlocality in noncommutative theories.

One-loop perturbative corrections reveal dependence on noncommutativity parameter.

Method has potential applications in realistic phenomenological models.

Abstract

We study noncommutative field theories, which are inherently nonlocal, using a Poincar\'e-invariant regularisation scheme which yields an effective, nonlocal theory for energies below a cut-off scale. After discussing the general features and the peculiar advantages of this regularisation scheme for theories defined in noncommutative spaces, we focus our attention onto the particular case when the noncommutativity parameter is inversely proportional to the square of the cut-off, via a dimensionless parameter $\eta$. We work out the perturbative corrections at one-loop order for a scalar theory with quartic interactions, where the signature of noncommutativity appears in $\eta$-dependent terms. The implications of this approach, which avoids the problems related to UV-IR mixing, are discussed from the perspective of the Wilson renormalisation program. Finally, we remark about the generality of the method, arguing that it may lead to phenomenologically relevant predictions, when applied to realistic field theories.