Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2000-12-29
Phys.Lett. B511 (2001) 101-111
Physics
High Energy Physics
High Energy Physics - Theory
21 pages, latex, no figures, shortened version to appear in Physics Letters B
Scientific paper
10.1016/S0370-2693(01)00627-X
We develop a systematic perturbative expansion and compute the one-loop two-points, three-points and four-points correlation functions in a non-commutative version of the U(N) Wess-Zumino-Witten model in different regimes of the $\theta$-parameter showing in the first case a kind of phase transition around the value $\theta_c = \frac{\sqrt{p^2 + 4 m^2}}{\Lambda^2 p}$, where $\Lambda$ is a ultraviolet cut-off in a Schwinger regularization scheme. As a by-product we obtain the functions of the renormalization group, showing they are essentially the same as in the commutative case but applied to the whole U(N) fields; in particular there exists a critical point where they are null, in agreement with a recent background field computation of the beta-function, and the anomalous dimension of the Lie algebra-valued field operator agrees with the current algebra prediction. The non-renormalization of the level $k$ is explicitly verified from the four-points correlator, where a left-right non-invariant counter-term is needed to render finite the theory, that it is however null on-shell. These results give support to the equivalence of this model with the commutative one.
No associations
LandOfFree
Correlation functions in the non-commutative Wess-Zumino-Witten model does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Correlation functions in the non-commutative Wess-Zumino-Witten model, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Correlation functions in the non-commutative Wess-Zumino-Witten model will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-12082