ON THE ALGEBRAIC STRUCTURE OF N = 2 STRING THEORY

In N = 2 string theory the chiral algebra expresses the generations and anti-generations of the theory and the Yukawa couplings among them and is thus crucial to the phenomenological properties of the theory. Also the connection with complex geometry is largely through the algebras. These algebras are systematically investigated in this paper. A solution for the algebras is found in the context of rational conformal field theory based on Lie algebras. A statistical mechanics interpretation for the chiral algebra is given for a large family of theories and is used to derive a rich structure of equivalences among the theories (dihedralities). The Poincare polynomials are shown to obey a resolution series which cast these in a form which is a sum of complete intersection Poincare polynomials. It is suggested that the resolution series is the proper tool for studying all N = 2 string theories and, in particular, exposing their geometrical nature.