Limits of conformal field theories (CFTs) are of great interest to physicists. In this talk I will first discuss the N-fold tensor product of a 2d CFT with itself. Next I will discuss the symmetric orbifold of such a tensor product, that is the CFT obtained by restricting to the subspace invariant under the symmetric group S_N. Finally I will describe how to define a limit CFT of this orbifold as N goes to infinity. In particular I will show that this
limit CFT factorizes, meaning its correlation functions can be
obtained by Wick contractions. This is joint work with Thomas
Gemuenden.