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**Two-dimensional models with \((0,2)\) supersymmetry: perturbative aspects.**
*(English)*
Zbl 1200.17014

In this impressive paper, the author presents a very interesting and important connection between quantum sigma models with \((0,2)\)-supersymmetry from the perspective of the theory of sheafs of chiral differential operators. Although the latter theory is known in the mathematical literature [V. Gorbounov, F. Malikov, V. Schechtman, “Gerbes of chiral differential operators.” Math. Res. Lett. 7, No. 1, 55–66 (2000; Zbl 0982.17013)], the approach developed is less known in the physics literature. This ansatz, in perturbation theory, among many interesting facts, leads to a new perspective of quantum field theories. The perturbation theory of such quantum field theories also admits an ech-type description, which further allows various technical simplifications. For these free field theories, analyzed from this ‘point of view, fermions can be neglected and bosons be described by means of a special free field theory. Obstructions to neutrality and existence conditions of Virasoro fields as anomaly cancellation are described in detail. Various examples are developed to clarify this technique. This extraordinary work constitutes a novel approach to sigma models (with the constraint of perturbation theory), and certainly opens new possibilities for their physical understanding with heavy mathematical machinery.

Reviewer: Rutwig Campoamor-Stursberg (Madrid)

### MSC:

17B69 | Vertex operators; vertex operator algebras and related structures |

81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |

81T60 | Supersymmetric field theories in quantum mechanics |

17B81 | Applications of Lie (super)algebras to physics, etc. |