Type II Duality Symmetries in Six Dimensions

TL;DR

This paper explores the discrete duality symmetries in six-dimensional string theories originating from different 10D string compactifications, revealing their group-theoretical structure and providing explicit duality transformation rules.

Contribution

It uncovers the group-theoretical foundation of six-dimensional duality symmetries and derives explicit transformation rules applicable to various backgrounds.

Findings

Identifies the cubic group ${ m C}/\Z_2$ as the structure governing dualities.

Provides explicit rules for constructing duality transformations.

Applies rules to generate dual models of the 6D chiral null background.

Abstract

We discuss the different discrete duality symmetries in six dimensions that act within and between (i) the 10-dimensional heterotic string compactified on $T^4$, (ii) the 10-dimensional Type IIA string compactified on $K3$ and (iii) the 10-dimensional Type IIB string compactified on $K3$. In particular we show that the underlying group-theoretical structure of these discrete duality symmetries is determined by the proper cubic group ${\cal C}/\Z_2$. Our group theoretical interpretation leads to simple rules for constructing the explicit form of the different discrete Type II duality symmetries in an arbitrary background. The explicit duality rules we obtain are applied to construct dual versions of the 6-dimensional chiral null model.