A note on M(atrix) theory in seven dimensions with eight supercharges

TL;DR

Seven-dimensional M-theory compactifications with eight supercharges are analyzed, with a conjecture that M(atrix) theory on $K3$ and Heterotic M(atrix) theory on $T^3$ share a common $5+1$-dimensional fixed point theory. This theory has base $\widetilde{S}^1\times \widetilde{K3}$ and arises from Rozali's emergent dimension, realizing the $SL(5,Z)$ U-duality as a coordinate exchange. The paper derives how heterotic and K3 data map to seven-dimensional duality, obtaining $\alpha' \sim V'_{K3}$ and $\lambda_7 \sim (V'_{K3})^{3/4}$ with $V_{T^3}$ fixed. The discussion hints at a wrapped M5-brane worldvolume interpretation and outlines future work to relate non-orbifold K3 and to sharpen the worldvolume description.

Abstract

We consider M(atrix) theory compactifications to seven dimensions with eight unbroken supersymmetries. We conjecture that both M(atrix) theory on K3 and Heterotic M(atrix) theory on T^3 are described by the same 5+1 dimensional theory with N=2 supersymmetry which is broken to N=1 by the base space. The emergence of the extra dimension follows from a recent result of Rozali[hep-th/9702136]. We show that the seven dimensional duality between M-theory on K3 and Heterotic string theory on T^3 is realised in M(atrix) theory as the exchange of one of the dimensions with this new dimension.