space dimension and has no tachyons. While fermionic worldsheet degrees of freedom are certainly needed for phenomenological reasons, our solution shows that supersymmetry is not required in all representations of quantum string theory (the degrees of freedom do not necessarily form a supersymmetry multiplett).

One may ask how these celebrated predictions of string theory, 1. a critical dimension of $D=26$ for the bosonic string and $D=10$ for the superstring are circumvented. The answer is very simple: In the sense of our defintion, the representation used in ordinary string theory is rather unnatural both from the point of view of AQFT and and LQG: From the point of view of AQFT, the usual Fock representation of string theory does not manifestly define a positive linear functional on the corresponding $^\ast-$algebra. It is therefore not surprising that the “no – ghost theorem” only holds in critical dimensions and that our solution to a manifestly ghost – free problem works in any dimension. From the LQG point of view on the other hand the implementation of the constraints in ordinary string theory is rather unnatural because a) one works in a particular worldsheet gauge thus breaking worldsheet diffeomorphism invarinance down to the conformal 