Exact Results for N=2 Compactifications of Heterotic Strings

TL;DR

This paper explores dualities between heterotic and type II string compactifications with N=2 supersymmetry, providing exact non-perturbative superpotentials and connecting different moduli spaces, thus deepening understanding of string dualities and N=2 theories.

Contribution

It presents explicit examples of N=2 heterotic and type II dual pairs, revealing exact superpotentials and elucidating moduli space connections, extending Seiberg-Witten results with stringy corrections.

Findings

Concrete heterotic/type II dual pairs constructed

Exact non-perturbative superpotentials derived

Moduli space connections between different N=2 vacua analyzed

Abstract

We search for $N=2$, $d=4$ theories which can be realized both as heterotic string compactifications on $K_{3}\times T^{2}$ and as type II string compactifications on Calabi-Yau threefolds. In such cases, the exact non-perturbative superpotential of one string theory is given in terms of tree level computations in the other string theory. In particular we find concrete examples which provide the stringy realization of the results of Seiberg and Witten on N=2 Yang-Mills theory, corrected by gravitational/stringy effects. We also discuss some examples which shed light on how the moduli spaces of different N=2 heterotic vacua are connected.