An introduction to quantum sheaf cohomology

Sharpe, Eric

Annales de l'Institut Fourier, Tome 61 (2011) no. 7, pp. 2985-3005.

Dans ces notes nous passons en revue la « cohomologie quantique des faisceaux », une déformation de la cohomologie des faisceaux qui apparaît d’une façon similaire à la cohomologie quantique ordinaire (tout en la généralisant parfois). La cohomologie quantique des faisceaux apparaît dans l’étude de la symétrie miroir (0,2), ce qui est passé en revue. Après ça nous passons en revue la théorie standard des champs topologique et les modèles A/2, B/2, dans lesquels la cohomologie quantique des faisceaux apparaît, et esquissons les définitions basiques et les calculs. Ensuite nous discutons dans ce contexte les modèles de supersymétrie Landau-Ginzburg (2,2) et (0,2) ainsi que la cohomologie quantique des faisceaux.

In this note we review “quantum sheaf cohomology,” a deformation of sheaf cohomology that arises in a fashion closely akin to (and sometimes generalizing) ordinary quantum cohomology. Quantum sheaf cohomology arises in the study of (0,2) mirror symmetry, which we review. We then review standard topological field theories and the A/2, B/2 models, in which quantum sheaf cohomology arises, and outline basic definitions and computations. We then discuss (2,2) and (0,2) supersymmetric Landau-Ginzburg models, and quantum sheaf cohomology in that context.

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