# Feynman diagrams: Planar Vs Non-Planar topologies

Sleuth
Hi everybody,
as usual I need help with some definitions regarding many-loop calculations.

In particular what do we mean with planar and non-planar topologies exactly?
I have an idea but I'm really not sure how to formalize it for an arbitrary big number of loops and legs.

Second, once the definition is taken, which different difficulties have to be overcome in the evaluations of the planar and non-planar topologies? I ask this simply because I notice that usually the big calculations are done dividing the two contributions and analyzing them in different steps. Why is it so?

Thank you very much

Sleuth

I am not sure what you mean by planar.

There is a rather old paper by t'Hooft showing that planar graphs in SU(N) gauge theories are related to the so-called large-N limit (which is 1/N = 1/3 ~ 0 in QCD :-) These planar graphs are equivalent to a theory of weakly interacting mesons generated by bilinear fermionic operators.

I can't remeber the details, but perhaps this helps.

Sleuth
I don't know either :P
I'm reading some papers about multi-loop qcd calculations, for example consider the process
e+ e- --> q,qbar,g at 2 loops in qcd

to analyze this process in the paper they consider

gamma* --> q,qbar,g at two loops

in the calculations they wrote two different papers about the evaluation of the planar and non-planar diagrams, without giving a definition, as it was something trivial or known somehow...

http://arxiv.org/pdf/hep-ph/0101124
http://arxiv.org/pdf/hep-ph/0008287

can u understand anything ? :P

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