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Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes

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We develop techniques to compute higher loop string amplitudes for twistedN=2 theories withĉ=3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured to all orders by a master anomaly equation. In a particular realization of theN=2 theories, the resulting string field theory is equivalent to a topological theory in six dimensions, the Kodaira-Spencer theory, which may be viewed as the closed string analog of the Chern-Simons theory. Using the mirror map this leads to computation of the ‘number’ of holomorphic curves of higher genus curves in Calabi-Yau manifolds. It is shown that topological amplitudes can also be reinterpreted as computing corrections to superpotential terms appearing in the effective 4d theory resulting from compactification of standard 10d superstrings on the correspondingN=2 theory. Relations withc=1 strings are also pointed out.

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Author notes

  1. S. Cecotti

    Present address: Direzione Regionale per la Autonomie Locali, via A. Caccia 17, I-33100, Udine, Italy

Authors and Affiliations

  1. Lyman Laboratory of Physics, Harvard University, 02138, Cambridge, MA, USA

    M. Bershadsky

  2. SISSA-ISAS and INFN sez. di Trieste, Trieste, Italy

    S. Cecotti

  3. RIMS, Kyoto University, 606-01, Kyoto, Japan

    H. Ooguri

  4. Lyman Laboratory of Physics, Harvard University, 02138, Cambridge, MA, USA

    C. Vafa

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Communicated by R.H. Dijkgraaf

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Bershadsky, M., Cecotti, S., Ooguri, H. et al. Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes. Commun.Math. Phys. 165, 311–427 (1994). https://doi.org/10.1007/BF02099774

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