On toroidal compactification of heterotic superstrings

I comment on the use of background gauge fields and antisymmetric tensor fields in toroidal compactification of heterotic strings, and explicitly construct the background gauge field that interpolates between the ${\mathrm{E}}_8$×${\mathrm{E}}_8$ and Spin(32)/$Z_2$ theories defined on $R^9$×$S^1$.