Worldline approach to the Grosse-Wulkenhaar model

FRANCHINO VIÑAS; P A G PISANI

JOURNAL OF HIGH ENERGY PHYSICS - (Online)

Springer Berlin Heidelberg

Año: 2014 vol. 1411 p. 87 - 109

1029-8479

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 β-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.