Physical Spectrum of Compactified Strings

The single-particle states of compactified bosonic string theory are classified by a direct product of a fundamental representation of the Heisenberg algebra for the noncompact flat dimensions and an affine-$g$ Lie algebra, where the rank of its Lie subalgebra $g$ is the number of internal dimensions and its identity depends on their length scales. The operators that create these states are explicitly constructed in light-cone gauge. The massless particles lie in the adjoint representation of $g$.