# Is there a maximum number of fixed points that a QFT can have?

I was wondering: is there a maximum number of (trivial and non-trivial) fixed points that a QFT can have (as a function of the space-time dimension and field content in the QFT)?

• Not really. There are theories with a continuous line of fixed points. – SM Kravec Jul 8 '15 at 20:49
• @SM Kravec : But I thought the continuous line of fixed point comes in the limit of $N \rightarrow \infty$. – Jaswin Jul 9 '15 at 7:20
• What's N? Generically you get a line of fixed points when there's an exactly marginal operator. The theory of a compact boson in D=1+1 has this. Higher dimensional examples tend to have supersymmetry. – SM Kravec Jul 9 '15 at 19:04