Planar Dominance in Non-commutative Field Theories at Infinite External Momentum

Details Planar Dominance in Non-commutative Field Theories at Infinite External Momentum Planar Dominance in Non-commutative Field Theories at Infinite External Momentum

2005-09-30

arxiv.org/abs/hep-th/0509229v2

Prog.Theor.Phys. 115 (2006) 217-228

Physics

High Energy Physics

High Energy Physics - Theory

14 pages, 7 Figures

Scientific paper

10.1143/PTP.115.217

In perturbative expansion of field theories on a non-commutative geometry, it is known that planar diagrams dominate when the non-commutativity parameter $\theta$ goes to infinity. We discuss whether the ``planar dominance'' occurs also in the case where $\theta$ is finite, but the external momentum goes to infinity instead. While this holds trivially at the one-loop level, it is not obvious at the two-loop level in particular in the presence of UV divergences. We perform explicit two-loop calculations in the six-dimensional $\phi^3$ theory, and confirm that nonplanar diagrams after renormalization do vanish in the above limit.

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