We combine I. background independent Loop Quantum Gravity ( LQG ) 
quantization techniques , II .
the mathematically rigorous framework of Algebraic Quantum Field Theory ( AQFT ) and III .
the theory of integrable systems resulting in the invariant Pohlmeyer Charges in order to set up the general representation theory ( superselection theory ) for the closed bosonic quantum string on flat target space .

While we do not solve the , expectedly , rich representation theory completely , we present a , to the best of our knowledge new , non – trivial solution to the representation problem .
This solution exists 1. for any target space dimension , 2. for Minkowski signature of the target space , 3. without tachyons , 4. manifestly ghost Рfree ( no negative norm states ) , 5. without fixing a worldsheet or target space gauge , 6. without ( Virasoro ) anomalies ( zero central charge ) , 7. while preserving manifest target space Poincar̩ invariance and 8. without picking up UV divergences .

The existence of this stable solution is , on the one hand , exciting because it raises the hope that among all the solutions to the representation problem ( including fermionic degrees of freedom ) we find stable , phenomenologically acceptable ones in lower dimensional target spaces , possibly without supersymmetry , that are much simpler than the solutions that arise via compactification of the standard Fock representation of the string .
On the other hand , if such solutions are found , then this would prove that neither a critical dimension ( D=10,11,26 ) nor supersymmetry is a prediction of string theory .
Rather , these would be features of the particular Fock representation of current string theory and hence would not be generic .

The solution presented in this paper exploits the flatness of the target space in several important ways .
In a companion paper we treat the more complicated case of curved target spaces .