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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ArXiv ePrint: 1406.7336
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Viñas, S.F., Pisani, P. Worldline approach to the Grosse-Wulkenhaar model. J. High Energ. Phys. 2014, 87 (2014). https://doi.org/10.1007/JHEP11(2014)087
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DOI: https://doi.org/10.1007/JHEP11(2014)087