Toroidal compactification of non-supersymmetric heterotic strings

We show that all the recently discovered rank-16 non-supersymmetric heterotic strings form a single connected class of theories when compactified on tori in the presence of constant background fields. In addition we show that in a weaker sense all the heterotic theories compactified on tori are connected. We also discuss the dependence of the higher loop amplitudes in the heterotic string on the background fields, and show that whenever the compactified theory has an enhanced gauge symmetry without U(1) factors, the cosmological constant to all loops is an extremum with respect to the background field expectation values. (orig.)