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Supersymmetry of the chiral de Rham complex. (English) Zbl 1205.17028

In the paper under review, the authors give a formulation of the chiral de Rham complex, introduced in [F. Malikov, V. Schechtman and A. Vaintrob, Commun. Math. Phys. 204, No. 2, 439–473 (1999; Zbl 0952.14013)], in terms of supersymmetric vertex algebras from [R. Heluani and V. G. Kac, Commun. Math. Phys. 271, No. 1, 103–178 (2007; Zbl 1205.17029)]. This formalism yields certain simplifications in the description of the chiral de Rham complex. Using that superfield formulation, the authors construct \(N=1,2,4\) superconformal structures on the chiral de Rham complex.

MSC:

17B69 Vertex operators; vertex operator algebras and related structures
14F40 de Rham cohomology and algebraic geometry
81T60 Supersymmetric field theories in quantum mechanics
53C26 Hyper-Kähler and quaternionic Kähler geometry, “special” geometry
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