Dual Pairs of Type II String Compactification

TL;DR

The paper investigates dualities among Type II string compactifications by exploiting the six‑dimensional $U$‑duality and an adiabatic argument to generate dual pairs in lower dimensions. It identifies a specific $SO(5,5;\mathbb{Z})$ element, $\bar{\Omega}_0$, that conjugates $SO(4,4)$ T‑duality and exchanges NS‑NS with RR sectors, enabling construction of $d=4$ theories with $N=6$, $N=4$, and $N=2$ (and potentially $N=1$) supersymmetry and a rich set of self‑dual examples. The authors develop a general method for producing dual pairs via conjugation and circle reductions, yielding explicit models where $S$ and $T$ moduli are exchanged and the surviving duality group is constrained to subgroups like $\Gamma_0(n)$. They provide numerous explicit four‑dimensional duals (and six‑dimensional cases), analyze their spectra, gauge contents, and enhanced symmetry points, and illustrate how perturbative spectra match while certain features are nonperturbative in the dual theory, making this a practical laboratory for testing duality conjectures.

Abstract

Using a $U$-duality symmetry of type II compactification on $T^4$ represented by triality action on the $T$-duality group, and applying the adiabatic argument we construct dual pairs of type II compactifications in lower dimensions. The simplicity of this construction makes it an ideal set up for testing various conjectures about string dualities. In some of these models the type II string has a perturbative non-abelian gauge symmetry. Examples include models with $N=2,4,6$ supersymmetry in four dimensions. There are also self-dual (in the sense of $S-T$ exchange symmetric) $N=2$ and $N=6$ examples. A generalization of the adiabatic argument can be used to construct dual pairs of models with $N=1$ supersymmetry.