Deformations of Topological Open Strings

Details Deformations of Topological Open Strings Deformations of Topological Open Strings

2000-06-16

arxiv.org/abs/hep-th/0006120v3

JHEP 0101:035,2001

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX 30 pages, corrected typos

Scientific paper

10.1088/1126-6708/2001/01/035

Deformations of topological open string theories are described, with an emphasis on their algebraic structure. They are encoded in the mixed bulk-boundary correlators. They constitute the Hochschild complex of the open string algebra -- the complex of multilinear maps on the boundary Hilbert space. This complex is known to have the structure of a Gerstenhaber algebra (Deligne theorem), which is also found in closed string theory. Generalising the case of function algebras with a B-field, we identify the algebraic operations of the bulk sector, in terms of the mixed correlators. This gives a physical realisation of the Deligne theorem. We translate to the language of certain operads (spaces of d-discs with gluing) and d-algebras, and comment on generalisations, notably to the AdS/CFT correspondence. The formalism is applied to the topological A- and B-models on the disc.

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