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On operad structures of moduli spaces and string theory

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We construct a real compactification of the moduli space of punctured rational algebraic curves and show how its geometry yields operads governing homotopy Lie algebras, gravity algebras and Batalin-Vilkovisky algebras. These algebras appeared recently in the context of string theory, and we give a simple deduction of these algebraic structures from the formal axioms of conformal field theory and string theory.

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Authors and Affiliations

  1. Department of Mathematics, University of North Carolina, 27599-3250, Chapel Hill, NC, USA

    Takashi Kimura & Jim Stasheff

  2. Department of Mathematics, University of Pennsylvania, 19104-6395, Philadelphia, PA, USA

    Takashi Kimura & Alexander A. Voronov

  3. Department of Mathematics, Princeton University, 08544-1000, Princeton, NJ, USA

    Alexander A. Voronov

Authors
  1. Takashi Kimura
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  2. Jim Stasheff
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  3. Alexander A. Voronov
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Additional information

Communicated by R.H. Dijkgraaf

To the memory of Ansgar Schnizer

Research supported by an NSF Postdoctoral Research Fellowship

Research supported in part by NSF grant DMS-9206929 and a Research and Study Leave from the University of North Carolina-Chapel Hill

Research supported in part by NSF grant DMS-9108269.A03

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Kimura, T., Stasheff, J. & Voronov, A.A. On operad structures of moduli spaces and string theory. Commun.Math. Phys. 171, 1–25 (1995). https://doi.org/10.1007/BF02103769

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