Anatomy of a Duality

TL;DR

This paper explores the duality relations and matrix theory formulations of M-theory compactified on K3 X I, proposing a new approach involving D-branes, orientifolds, and the little heterotic string to understand its non-perturbative structure.

Contribution

It introduces a novel matrix theory framework for M-theory on K3 X I using D-branes and orientifolds, linking it to six-dimensional heterotic string theories.

Findings

Identifies string dualities between different compactifications.

Proposes a matrix theory description via large N limits of orientifold models.

Suggests a complete matrix theory involves the little heterotic string on a dual surface.

Abstract

The nature of M-theory on K3 X I, where I is a line interval, is considered, with a view towards formulating a `matrix theory' representation of that situation. Various limits of this compactification of M-theory yield a number of well known N=1 six dimensional compactifications of the heterotic and type I string theories. Geometrical relations between these limits give rise to string/string dualities between some of these compactifications. At a special point in the moduli space of compactifications, this motivates a partial definition of the matrix theory representation of the M-theory on K3 X I as the large N limit of a certain type IA orientifold model probed by a conglomerate of N D-branes. Such a definition in terms of D-branes and orientifold planes is suggestive, but necessarily incomplete, due to the low amount of superymmetry. It is proposed - following hints from the orientifold model - that the complete matrix theory representation of the K3 X I compactified M-theory is given by the large N limit of compactification - on a suitable `dual' surface - of the `little heterotic string' N = 1 six dimensional quantum theories.