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On the Relation Between Open and Closed Topological Strings

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Abstract

We discuss the relation between open and closed string correlators using topological string theories as a toy model. We propose that one can reconstruct closed string correlators from the open ones by considering the Hochschild cohomology of the category of D-branes. We compute the Hochschild cohomology of the category of D-branes in topological Landau-Ginzburg models and partially verify the conjecture in this case.

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Authors and Affiliations

  1. Department of Physics, California Institute of Technology, Pasadena, CA, 91125, USA

    Anton Kapustin

  2. Department of Mathematics, University of North Carolina, Chapel Hill, NC, 27599, USA

    Lev Rozansky

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  1. Anton Kapustin
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  2. Lev Rozansky
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Correspondence to Anton Kapustin.

Additional information

Communicated by M.R. Douglas

Acknowledgement A.K. would like to thank Volodya Baranovsky, Ezra Getzler, Kentaro Hori, Dima Orlov, and Sasha Voronov for help at various stages. A.K. is also grateful to the Department of Mathematics of Northwestern University and the Erwin Schrödinger Institute for hospitality while this work was being completed. L. R. is very grateful to Mikhail Khovanov for numerous discussions of the category of matrix factorizations. This work was supported in part by the DOE grant DE-FG03-92-ER40701 and by the NSF grant DMS-0196131.

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Kapustin, A., Rozansky, L. On the Relation Between Open and Closed Topological Strings. Commun. Math. Phys. 252, 393–414 (2004). https://doi.org/10.1007/s00220-004-1227-z

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