Worldline approach to the Grosse-Wulkenhaar model

Understand

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.