String with noncommutative world-sheet and stringy instantons

The model of the bosonic string with the noncommutative world-sheet geometry is proposed in the framework of Fedosovʹs deformation quantization. The re-interpretation of the model in terms of bosonic string coupled to infinite multiplet of background fields is given and the link to the W-symmetry is discussed. For the case of d=4 Euclidean target space, the stringy counterparts of the Yang–Mills instantons are constructed in both commutative and noncommutative regimes.