  We establish rigorous error bounds for approximating correlation functions of
conformal field theories (CFTs) by certain finite-dimensional tensor networks.
For chiral CFTs, the approximation takes the form of a matrix product state.
For full CFTs consisting of a chiral and an anti-chiral part, the approximation
is given by a finitely correlated state. We show that the bond dimension scales
polynomially in the inverse of the approximation error and sub-exponentially in
the ultraviolett cutoff. We illustrate our findings using Wess-Zumino-Witten
models, and show that there is a one-to-one correspondence between
group-covariant MPS and our approximation.
