Worldline approach to the Grosse-Wulkenhaar model

Sebastián Franchino Viñas; Pablo Pisani

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arXiv · 1406.7336

Worldline approach to the Grosse-Wulkenhaar model

Sebastián Franchino Viñas·Pablo Pisani

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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 $β$-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.

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Sebastián Franchino Viñas, Pablo Pisani. 2014-12-05. Worldline approach to the Grosse-Wulkenhaar model. https://arxiv.org/abs/1406.7336

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