Comments on perturbative dynamics of non-commutative Yang–Mills theory
By Adi Armoni. 2000
201 citations recorded by the source corpus.
Abstract We study the U(N) non-commutative Yang–Mills theory at the one-loop approximation. We check renormalizability and gauge invariance of the model and calculate the one-loop beta function. The interaction of the SU(N) gauge bosons with the U(1) gauge boson plays an important role in the consistency check. In particular, the SU(N) theory by itself is not consistent. We also find that the θ→0 limit of the U(N) theory does not converge to the ordinary SU(N)×U(1) commutative theory, even at the planar limit. Finally, we comment on the UV/IR mixing.
Subfields: Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/985eb3c45e458565dc0af1d9a7e53913041be772
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Citations in the corpus
- Quantum field theory on noncommutative spaces (2001, methodology): “This can be done in a straightforward way by adapting the standard Faddeev-Popov technique to the noncommutative case [91, 104, 107].”
- NonAbelian noncommutative gauge theory via noncommutative extra dimensions (2001, background): “Aspects of the quantization of nonabelian noncommutative gauge theories have been discussed by several authors [24, 25 , 26] (and references therein.) Closest to the present discussion is the perturbative study of θ-expanded noncommutative gauge theories [27, 28].”
- Noncommutative field theory (2001, background): “ is not visible in the prepotential, which is independent of the diagonal component of the scalar vev. This sector (and the rank 1 theory) is nontrivial, and does not reduce to Maxwell theory as θ→0 (Armoni, 2001). It is not understood at present. Noncommutative sigma models are discussed by Lee, Le”
- Emergent geometry and gravity from matrix models: an introduction (2010, background): “This implies that a UV–divergence in some direction kμ ΛNC is necessarily associated with an IR effect in another direction; this is the essence of UV/IR mixing [73].”
- Conformal anomalies in noncommutative gauge theories (2001, unknown): “26) includes the non-planar contribution [19] [13].”
- Review of the phenomenology of noncommutative geometry (2002, background): “There has already been extensive work on scalar field theory [21, 22, 23], NCQED (the noncommutative analog of QED) [24, 25], as well as noncommutative Yang-Mills [26, 27]; perturbation theory in θ is applicable and the theories are renormalizable [28, 29].”