Wrapping the M Theory Five-Brane on K3

TL;DR

The paper addresses how M-theory physics emerges as the heterotic string in seven dimensions by wrapping the M5-brane on $K3$. It develops a covariant PST-based M5-brane action and a $T$-duality–invariant Narain string action, enabling a direct comparison between the dual descriptions. The authors show that double dimensional reduction on $K3$ yields the bosonic heterotic string in $7d$, with Narain moduli $L_{IJ}$ and $M_{IJ}$ arising from harmonic forms on $K3$ and a volume scaling ${\cal V} \sim \lambda_H^{4/3}$ relating the 7d and 11d metrics. This work clarifies the heterotic/M-theory duality and provides a covariant, duality-symmetric framework for Narain-compactified heterotic strings, highlighting how moduli and volumes map across the dual theories.

Abstract

Using a recently constructed M5-brane world-volume action, we demonstrate that wrapping the M5-brane on K3 gives the heterotic string in seven dimensions. To facilitate the comparison, a new version of the world-sheet action for the Narain-compactified heterotic string, with manifest T duality invariance, is formulated.