Ten-dimensional Superstring theory unifies the Standard Model and quantum gravity. To obtain a four-dimensional theory with Space-Time Supersymmetry (which is necessary for phenomenological reasons), as shown by Candelas, Horowitz, Strominger, Witten, we must compactify six of the ten dimensions on a so-called Calabi-Yau manifold. Another equivalent approach to do the same is the compactification of 6 dimensions into an 𝑁=2 Superconformal field theory with the central charge 𝑐=9, as was shown by D. Gepner. Each of these two equivalent approaches has its own merits. In particular, Gepner's approach makes it possible to use exactly solvable N=2 SCFT models and thus obtain an explicit solution of the considered model. The subject of my talk is a new approach to the construction of Calabi-Yau orbifolds of Fermat type required for the compactification in Superstring theory. The idea of the approach is to use the connection of the CY orbifolds with a class of exactly solvable N=2 SCFT models for explicitly constructing a complete set of fields in these orbifold models using the Spectral flow twist (Schwimmer and Seiberg) and the requirement of the mutual locality of the fields.
De Nathan Seiberg
De Vijay Balasubramanian
De Steve Zelditch
De Eva Silverstein
De Eliezer Rabinovici
De Alexander Gorsky
De Rémi Monasson
De David McAllester
De Luca Mazzucato
De Alexander Belavin
De Washington Taylor
De Gérard Ben Arous
