M-theory/heterotic Duality: a Kaluza-Klein Perspective

TL;DR

This work provides a comprehensive, group-theoretic account of classical M-theory/heterotic duality via KK reductions on K3 and T^3. By employing solvable Lie algebras and explicit coset constructions, it unifies the scalar sector descriptions across D≥3, revealing O(10−D,10−D+N) type symmetries and their Iwasawa decompositions in the heterotic theory, while detailing the intricate mapping to M-theory on K3. The authors also analyze the charge lattices and p-brane orbits, showing consistent duality of M-theory and heterotic charges, and discuss the role of Eguchi–Hanson resolutions in K3 as a bridge to the heterotic spectrum, including the subtle issues of KK truncation consistency. The results illuminate how duality interchanges strong/weak coupling regimes and how supersymmetric YM-derived p-branes relate to wave-like ten-dimensional configurations, with implications for non-perturbative structure in string/M-theory. Overall, the paper provides explicit, solvable-algebra-based constructions that underpin the classical M-theory/heterotic duality and its consequences for scalar cosets, charge lattices, and p-brane spectra.

Abstract

We study the duality relationship between M-theory and heterotic string theory at the classical level, emphasising the transformations between the Kaluza-Klein reductions of these two theories on the K3 and T^3 manifolds. Particular attention is devoted to the corresponding structures of sigma-model cosets and the correspondence between the p-brane charge lattices. We also present simple and detailed derivations of the global symmetries and coset structures of the toroidally-compactified heterotic theory in all dimensions D \ge 3, making use of the formalism of solvable Lie algebras.