Unification of String Dualities

TL;DR

This work argues that the entire web of conjectured dualities among string, M-, and F-theory can be generated from a small set of principles anchored to the ten-dimensional Type I – SO(32) heterotic duality and the definitions of M- and F-theories. It introduces a concrete derivation framework comprising rules such as unifying $S$- and $T$-dualities, duality of dualities, large-volume limits, and fiberwise duality, and then demonstrates explicit derivations for key dualities including string-string duality, Type IIB $SL(2,\mathbb{Z})$ S-duality, and M-/F-theory compactifications. The paper provides detailed, step-by-step derivations for M-theory on orbifolds and Hořava–Witten scenarios, as well as F-theory/heterotic dualities, showing that seemingly disparate dualities are interconnected manifestations of a single underlying structure. By reducing the landscape to a minimal set of nonperturbative anchors and transformation rules, it highlights a coherent organization of the moduli space and insights into the nonperturbative dynamics of string theory.

Abstract

We argue that all conjectured dualities involving various string, M- and F- theory compactifications can be `derived' from the conjectured duality between type I and SO(32) heterotic string theory, T-dualities, and the definition of M- and F- theories. (Based on a talk given at the conference on `Advanced Quantum Field Theory', Le Londe-les-Maures, France, Aug.31-Sept.5, 1996, in memory of Claude Itzykson)