Aspects of Type I - Type II - Heterotic Triality in Four Dimensions

TL;DR

This paper explores the equivalence of Type I, Type II, and Heterotic superstring theories in four dimensions, focusing on their effective field theories, prepotentials, and the role of BPS states, confirming superstring triality in specific models.

Contribution

It demonstrates the matching of prepotentials across different string theories in four dimensions, providing evidence for superstring triality through detailed calculations of one-loop corrections and BPS state contributions.

Findings

Prepotentials in Type I, Type II, and Heterotic theories agree in certain limits.

Perturbative prepotential is determined by one-loop Planck mass corrections.

BPS states from D=6 modes govern threshold corrections.

Abstract

We discuss the equivalence between Type I, Type II and Heterotic N=2 superstring theories in four dimensions. We study the effective field theory of Type I models obtained by orientifold reductions of Type IIB compactifications on $K_3\times T^2$. We show that the perturbative prepotential is determined by the one-loop corrections to the Planck mass and is associated to an index. As is the case for threshold corrections to gauge couplings, this renormalization is entirely due to N=2 BPS states that originate from D=6 massless string modes. We apply our result to the so-called S-T-U model which admits simultaneous Type II and Heterotic descriptions, and show that all three prepotentials agree in the appropriate limits as expected from the superstring triality conjecture.