N=2 Heterotic Superstring and its Dual Theory in Five Dimensions

TL;DR

The paper explores a coherent five-dimensional duality framework linking a heterotic string on $K_3\times S_1$ to eleven-dimensional supergravity compactified on a Calabi–Yau threefold, with Type II duals in a large-volume limit. It develops the 5D vector-multiplet sector via a cubic prepotential ${\cal V}(X)$, demonstrates a vector–tensor duality to match heterotic data, and computes one-loop heterotic corrections that reproduce CY intersection numbers. A central finding is the existence of an $SU(2)$ enhancement at the radius $R=1$, accompanied by additional massless states and a discontinuity in ${\cal V}$, while conifold singularities are absent in five dimensions. The strong-coupling analysis, using 4D/Type II duals, reveals non-perturbative states that persist in 5D and clarifies the mapping of enhanced-symmetry points and singularities across dimensions, establishing a robust 5D duality web for CY compactifications.

Abstract

We study quantum effects in five dimensions in heterotic superstring theory compactified on K_3 x S_1 and analyze the conjecture that its dual effective theory is eleven-dimensional supergravity compactified on a Calabi-Yau threefold. This theory is also equivalent to type II superstring theory compactified on the same Calabi-Yau manifold, in an appropriate large volume limit. In this limit the conifold singularity disappears and is replaced by a singularity associated to enhanced gauge symmetries, as naively expected from the heterotic description. Furthermore, we exhibit the existence of additional massless states which appear in the strong coupling regime of the heterotic theory and are related to a different type of singular points on Calabi-Yau threefolds.