2001/10/15 by Guang-Hong Chen, Yong-Shi Wu
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Black Holes and Theoretical Physics #Critical exponent #Critical phenomena #Gravitational singularity #Group (periodic table) #Momentum (technical analysis) #Noncommutative algebraic geometry #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Noncommutative quantum field theory #Renormalization #Renormalization group #cond-mat.stat-mech #hep-th
paper · pdf · doi:10.1016/s0550-3213(01)00587-9
published as Nucl.Phys. B622 (2002) 189-214 · 37 pages, 4 figures
arxiv created 2001/10/15 · openalex publication_date 2002/02/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 Θ-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 νm and βk, whose values are determined to be 1/4 and 1/2, respectively, at mean-field level.