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arXiv · 0902.4888

Wilsonian Renormalization of Noncommutative Scalar Field Theory

Razvan Gurau·Oliver J. Rosten
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Abstract

Drawing on analogies with the commutative case, the Wilsonian picture of renormalization is developed for noncommutative scalar field theory. The dimensionful noncommutativity parameter, theta, induces several new features. Fixed-points are replaced by `floating-points' (actions which are scale independent only up to appearances of theta written in cutoff units). Furthermore, it is found that one must use correctly normalized operators, with respect to a new scalar product, to define the right notion of relevance and irrelevance. In this framework it is straightforward and intuitive to reproduce the classification of operators found by Grosse & Wulkenhaar, around the Gaussian floating-point. The one-loop beta-function of their model is computed directly within the exact renormalization group, reproducing the previous result that it vanishes in the self-dual theory, in the limit of large cutoff. With the link between this methodology and earlier results made, it is discussed how the vanishing of the beta-function to all loops, as found by Disertori et al., should be interpreted in a Wilsonian framework.

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Razvan Gurau, Oliver J. Rosten. 2009-07-22. Wilsonian Renormalization of Noncommutative Scalar Field Theory. https://doi.org/10.1088/1126-6708/2009/07/064

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