C=1 conformal field theories on Riemann surfaces

Robbert Dijkgraaf, Erik Verlinde, Herman Verlinde

Research output: Contribution to journalArticlepeer-review

299 Scopus citations


We study the theory of c=1 torus and ℤ2-orbifold models on general Riemann surfaces. The operator content and occurrence of multi-critical points in this class of theories is discussed. The partition functions and correlation functions of vertex operators and twist fields are calculated using the theory of double covered Riemann surfaces. It is shown that orbifold partition functions are sensitive to the Torelli group. We give an algebraic construction of the operator formulation of these nonchiral theories on higher genus surfaces. Modular transformations are naturally incorporated as canonical transformations in the Hilbert space.

Original languageEnglish (US)
Pages (from-to)649-690
Number of pages42
JournalCommunications In Mathematical Physics
Issue number4
StatePublished - Dec 1988
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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