Heterotic Strings from Matrices

TL;DR

The paper provides a nonperturbative, matrix-model realization of heterotic string theory on $S^1/Z_2\times T^d$ by embedding Hořava–Witten domain walls into $O(M)$-gauged SUSY quantum mechanics and introducing 32 chiral fermions in the vector to cancel anomalies, thereby enabling an eleven-dimensional interpretation in certain limits and reproducing heterotic string Fock space from moduli-space dynamics. It extends to multidimensional toroidal compactifications where the low-energy theory on $S^1\times T^d/Z_2$ is described by a $U(M)$ gauge theory (reducing to $O(M)$ on orbifold circles), yielding heterotic and open-string sectors as distinct limits; twisted sectors (screwing) and GSO projections arise naturally from gauge structure. In the $d=1$ case and appropriate limits, the framework recovers both the $E_8\times E_8$ heterotic matrix model and Type $IA$ strings, with explicit open/closed-string constructions and unoriented variants. The work further speculates on a holographic mechanism for the cosmological constant problem and discusses how decompactification changes the degrees of freedom, suggesting deep connections between SUSY vacua, large-$N$ limits, and the underlying theory of quantum gravity, while highlighting outstanding technical challenges.

Abstract

We propose a nonperturbative definition of heterotic string theory on arbitrary multidimensional tori.