Conformal Field Theories on K3 and Three-Dimensional Gauge Theories

Abstract

According to a recent conjecture, the moduli space of the heterotic conformal field theory on a $G\subset$ ADE singularity of an ALE space is equivalent to the moduli space of a pure $\cx N=4$ supersymmetric three-dimensional gauge theory with gauge group G. We establish this relation using geometric engineering of heterotic strings and generalize it to theories with non-trivial matter content. A similar equivalence is found between the moduli of heterotic CFT on isolated Calabi--Yau 3-fold singularities and two-dimensional Kazama-Suzuki coset theories.

arXiv comment11pp, harvmac, v2: a relation between heterotic CFT on Calabi-Yau 3-fold singularities and Kazama-Suzuki models has been added

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• A new vista on the Heterotic Moduli Space from Six and Three Dimensions
• Heterotic-Type II duality in the hypermultiplet sector