String with noncommutative world-sheet and stringy instantons

TL;DR

This paper introduces a bosonic string model with a noncommutative world-sheet using Fedosov's deformation quantization, explores its relation to background fields and W-symmetry, and constructs stringy instantons in four-dimensional Euclidean space.

Contribution

It presents a novel noncommutative string model and links it to background fields and instanton solutions, expanding the understanding of noncommutative geometries in string theory.

Findings

Constructed stringy instantons in noncommutative 4D Euclidean space.

Reinterpreted the model in terms of background fields and W-symmetry.

Connected noncommutative world-sheet geometry with string instanton solutions.

Abstract

The model of the bosonic string with the noncommutative world-sheet geometry is proposed in the framework of Fedosov's 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.