Conformal Field Theories on K3 and Three-Dimensional Gauge Theories

TL;DR

This paper explores deep connections between heterotic conformal field theories on singular spaces and three-dimensional gauge theories, extending known dualities and establishing new geometric correspondences.

Contribution

It establishes a geometric engineering framework linking heterotic CFT moduli spaces to 3D gauge theories and generalizes the duality to include matter content.

Findings

Moduli space of heterotic CFT on ADE singularities matches 3D gauge theory moduli.

Generalization to theories with matter content broadens the duality.

Identifies equivalence between heterotic CFT on Calabi-Yau singularities and Kazama-Suzuki coset 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.