Worldline approach to the Grosse-Wulkenhaar model

TL;DR

This paper employs the worldline formalism to analyze the Grosse-Wulkenhaar model, deriving an efficient expression for the one-loop effective action and quantum corrections, with potential applications to noncommutative gauge theories.

Contribution

It introduces a novel application of the worldline approach to the Grosse-Wulkenhaar model, enabling straightforward computation of effective actions and quantum corrections.

Findings

Effective expression for the one-loop effective action

Quantum corrections to the background and beta-functions

Applicability to polynomial scalar field interactions

Abstract

We apply the worldline formalism to the Grosse-Wulkenhaar model and obtain an expression for the one-loop effective action which provides an efficient way for computing Schwinger functions in this theory. Using this expression we obtain the quantum corrections to the effective background and the $\beta$-functions, which are known to vanish at the self-dual point. The case of degenerate noncommutativity is also considered. Our main result can be straightforwardly applied to any polynomial self-interaction of the scalar field and we consider that the worldline approach could be useful for studying effective actions of noncommutative gauge fields as well as in other non-local models or in higher-derivative field theories.