Color Grosse-Wulkenhaar models: One-loop $β$-functions

Joseph Ben Geloun; Vincent Rivasseau

doi:10.1140/epjc/s10052-008-0708-1

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arXiv · 0805.2538

Color Grosse-Wulkenhaar models: One-loop $β$-functions

Joseph Ben Geloun·Vincent Rivasseau

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Abstract

The $β$-functions of O(N) and U(N) invariant Grosse-Wulkenhaar models are computed at one loop using the matrix basis. In particular, for ``parallel interactions", the model is proved asymptotically free in the UV limit for $N >1$, and has a triviality problem or Landau ghost for $N<1$. The vanishing $β$-function is recovered solely at N=1. We discuss various possible consequences of these results.

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Joseph Ben Geloun, Vincent Rivasseau. 2008-05-16. Color Grosse-Wulkenhaar models: One-loop $β$-functions. https://doi.org/10.1140/epjc%2Fs10052-008-0708-1

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