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Candidates for renormalisable gauge theory models on Moyal spaces constructed recently have non trivial vacua.
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E. Langmann, R. J. Szabo and K. Zarembo, “Exact solution of quantum field theory on noncommutative phase spaces,” JHEP 0401
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H. Grosse and R. Wulkenhaar, “The beta-function in duality-covariant noncommutative phi**4 theory,” Eur. Phys. J. C 35
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H. Grosse and R. Wulkenhaar, “Renormalisation of ϕ 4 \phi^{4} -theory on noncommutative ℝ 4 \mathbb{R}^{4} in the matrix base,” Commun. Math. Phys. 256
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2008
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