By ST we mean here old-fashioned perturbative string theory and not its (yet to be defined) M – Theory generalization.

In this paper we precisely define the general quantization problem for the closed, bosonic string on flat (Minkowski) target space. Namely, we set up the representation theory for the closed, bosonic string. We can fruitfully combine three different frameworks:

-   [I.]{} [*Background Independent LQG*]{}\
    The string can be viewed as a worldsheet diffeomorphism invariant, two – dimensional QFT. Hence it precisely falls into class of theories that can be quantized by LQG methods. Moreover, LQG provides a general framework for how to implement quantum constraints without gauge fixing.

-   [II.]{} [*Algebraic Quantum Field Theory (AQFT)*]{}\
    The Haag – Kastler  approach to QFT [@3] provides a clean distinction between the physical object to be quantized, namely the algebra of physical observables, and the corresponding set of representations (Hilbert spaces) thereof. The latter can be viewed as different phases of the the theory which may be or may be not realized in nature. AQFT provides very powerful tools in order to solve the classification problem of the corresponding representations, see e.g. [@4] for a recent review. For infinite dimensional systems such as 