Communications in Mathematical Physics

, Volume 165, Issue 2, pp 311–427

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

  • M. Bershadsky
  • S. Cecotti
  • H. Ooguri
  • C. Vafa

DOI: 10.1007/BF02099774

Cite this article as:
Bershadsky, M., Cecotti, S., Ooguri, H. et al. Commun.Math. Phys. (1994) 165: 311. doi:10.1007/BF02099774


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.

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • M. Bershadsky
    • 1
  • S. Cecotti
    • 2
  • H. Ooguri
    • 3
  • C. Vafa
    • 4
  1. 1.Lyman Laboratory of PhysicsHarvard UniversityCambridgeUSA
  2. 2.SISSA-ISAS and INFN sez. di TriesteTriesteItaly
  3. 3.RIMSKyoto UniversityKyotoJapan
  4. 4.Lyman Laboratory of PhysicsHarvard UniversityCambridgeUSA
  5. 5.Direzione Regionale per la Autonomie LocaliUdineItaly