Challenges and Simplifications of Large N Non-Abelian Gauge Theories

The difficulty stems from the lack of a small, dimensionless parameter which we can use as the basis for a perturbative expansion.

He pointed out that gauge theories based on the group G = SU(N) simplify in the limit N.

The theory simplifies in the large N limit because the collective behavior of the fields becomes stiffer as their number increases.

<p>The large N limit renders a theory tractable when the number of degrees of freedom grows linearly with N.</p> Signup and view all the answers

<p>Two examples are the CP N 1 model and the Gross-Neveu model.</p> Signup and view all the answers

<p>The theory simplifies but cannot be solved in the large N limit when the number of degrees of freedom grows as N^2 or faster.</p> Signup and view all the answers

<p>No, the large N limit is not likely to be relevant for QCD which has N = 3.</p> Signup and view all the answers

<p>No, the large N limit will not allow us to demonstrate confinement in Yang-Mills theory.</p> Signup and view all the answers

<p>There is no small, dimensionless parameter that can be used as the basis for a perturbative expansion.</p> Signup and view all the answers