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Renormalization of non-commutative quantum field theory (REN-NCFT)
Start date: Oct 1, 2007, End date: Sep 30, 2009 PROJECT  FINISHED 

This project aims at studying the renormalization of non-commutative field theories in a systematic way. Recently H. Grosse and R. Wulkenhaar proved that one can cure the IR/UV mixing of such theories by adding a new term in the Lagrangian. For the non-com mutative phi**4 theory, this harmonic potential term makes the theory renormalizable to all orders.An other model is renormalizable thanks to a similar procedure: the Gross-Neveu model on the Moyal plane. Nevertheless there is currently no way of computing the missing counterterm for other non-commutative spaces. The first part of the project will be devoted to the study of the space dependency of the renormalization procedure.We will consider different quartically interacting models (as phi**4 or Gross-Neveu) on non-commutative spaces and find the appropriate counterterms. The second part will concern the regularisation properties of non-commutative spaces. The non-commutative phi**4 model exhibits bounded renormalization group flow. In contrast its commutative counterpart has unbounded flow.The generality of such a feature will be studied. We also want to probe non-perturbative aspects of non-commutative field theories. We will use constructive techniques to define non-perturbatively such theories. Finally we want to examine the link between String theory and these new classes of non-commutative field theories.
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