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

Tadayuki Konagaya·Jun Nishimura
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Abstract

In perturbative expansion of field theories on a non-commutative geometry, it is known that planar diagrams dominate when the non-commutativity parameter $θ$ goes to infinity. We discuss whether the ``planar dominance'' occurs also in the case where $θ$ 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 $ϕ^3$ theory, and confirm that nonplanar diagrams after renormalization do vanish in the above limit.

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Tadayuki Konagaya, Jun Nishimura. 2006-02-01. Planar Dominance in Non-commutative Field Theories at Infinite External Momentum. https://doi.org/10.1143/ptp.115.217

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