Noncommutative Quantization in 2D Conformal Field Theory

The simplest possible noncommutative harmonic oscillator in two dimensions is used to quantize the free closed bosonic string in two flat dimensions. The nonsolitonic part of the partition function is not deformed by the introduction of noncommutativity, while the four point function is, preserving, nevertheless, the sl(2,C) invariance. Finally the first Ward identity of the deformed theory is derived