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 compactified on the torus. The partition function is not deformed by the introduction of noncommutativity, if we rescale the time by a factor that depends on the noncommutativity parameter and change the compactification radius appropriately. The four-point function and certain 2n-point functions are deformed, preserving, nevertheless, the sl(2,C) covariance.