# What's the radius of convergence for 1/N expansion in QCD?

I'm asking this question as someone who has not studied this topic technically. By radius of convergence, I mean exact results, not just approximations, can be obtained by summing sufficiently many terms. (does this ever happen?) I don't mind if you need 1000 terms, as long as the series is convergent mathematically. Is N=3 QCD within the radius of convergence? And how about N=2, N=1?

## Answers and Replies

Physics Monkey
There are lots of subtle issues relating to large N. For example, the limits $$T \rightarrow 0$$ and $$N \rightarrow \infty$$ may not commute. More generally, the limits of infinite volume and large N may not commute as in Eguchi-Kawai reduction. The limits $$\omega \rightarrow 0$$ and $$N \rightarrow \infty$$ relevant for response functions do not commute. There is plenty more.