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Prog. Theor. Phys. Vol. 115 No. 1 (2006) pp. 217-228
Planar Dominance in Non-Commutative Field Theories at Infinite External Momentum
Tadayuki Konagaya1,* and
Jun Nishimura1,2,**
1Department of Particle and Nuclear Physics,
The Graduate University for Advanced Studies (Sokendai),
Tsukuba 305-0801, Japan
2High Energy Accelerator Research Organization (KEK),
Tsukuba 305-0801, Japan
(Received September 16, 2005)
Abstract:
In the 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 investigate whether this “planar dominance” occurs also in the case that
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 φ3 theory and confirm
that nonplanar diagrams after renormalization do vanish in this limit.
URL :
http://ptp.ipap.jp/link?PTP/115/217/
DOI : 10.1143/PTP.115.217
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