Maximally Supersymmetric String Theories in D<10

TL;DR

This paper demonstrates the existence of maximally supersymmetric solutions in heterotic string theory beyond traditional toroidal compactifications, including explicit constructions in lower dimensions with specific gauge groups.

Contribution

It constructs an exact fermionic realization of an N=1 supersymmetric string theory in 8 dimensions with a non-simply-laced gauge group, expanding known solutions.

Findings

Existence of non-toroidal maximally supersymmetric solutions.

Explicit construction of an N=1 supersymmetric string in D=8 with Sp(20) gauge group.

Toroidal compactifications yield theories with reduced rank and extended supersymmetry.

Abstract

The existence of maximally supersymmetric solutions to heterotic string theory that are not toroidal compactifications of the ten-dimensional superstring is established. We construct an exact fermionic realization of an N=1 supersymmetric string theory in D=8 with non-simply-laced gauge group Sp(20). Toroidal compactification to six and four dimensions gives maximally extended supersymmetric theories with reduced rank (4,12) and (6,14) respectively.