Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2001-10-15
Nucl.Phys. B622 (2002) 189-214
Physics
High Energy Physics
High Energy Physics - Theory
37 pages, 4 figures
Scientific paper
10.1016/S0550-3213(01)00587-9
A one-loop renormalization group (RG) analysis is performed for noncommutative Landau-Ginsburg theory in an arbitrary dimension. We adopt a modern version of the Wilsonian RG approach, in which a shell integration in momentum space bypasses the potential IR singularities due to UV-IR mixing. The momentum-dependent trigonometric factors in interaction vertices, characteristic of noncommutative geometry, are marginal under RG transformations, and their marginality is preserved at one loop. A negative $\Theta$-dependent anomalous dimension is discovered as a novel effect of the UV-IR mixing. We also found a noncommutative Wilson-Fisher (NCWF) fixed point in less than four dimensions. At large noncommutativity, a momentum space instability is induced by quantum fluctuations, and a consequential first-order phase transition is identified together with a Lifshitz point in the phase diagram. In the vicinity of the Lifshitz point, we introduce two critical exponents $\nu_m$ and $\beta_k$, whose values are determined to be 1/4 and 1/2, respectively, at mean-field level.
Chen Guang-Hong
Wu Yong-Shi
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