content_image/326288.jpg content_image/326299.jpg content_image/326300.jpg content_image/326301.jpg content_image/326298.jpg content_image/326296.jpg content_image/326297.jpg
indices in the loop. Hence we have 

<img src='content_image/326288.jpg'>

<img src='content_image/326299.jpg'>

<img src='content_image/326300.jpg'>

<img src='content_image/326301.jpg'>

So a diagram with V vertices, E propagators and F loops will include a factor 

<img src='content_image/326298.jpg'>

where χ is the Euler characteristic of the diagram. It is a topological invariant, depending only on the genus (number of holes), g , of the surface: 

Therefore the perturbative expansion of any diagram in field theory can be written as 

<img src='content_image/326296.jpg'>

<img src='content_image/326297.jpg'>

where f$_{g}$ is some polynomial in λ . In the large N limit, we see that any computation will be dominated by those diagrams which are topologically 

