The bosonic string in D < 26 with and without Liouville fields

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It is shown that the Liouville modes for the bosonic string in D < 26 are equivalent to the old Brower modes. Consistent free quantum strings do therefore exist in D < 26 for all values of the Regge intercept α 0 such that α 0 ⩽ 1 for open strings and α 0 ⩽ 2 for closed strings, i.e. for all values allowed by the no-ghost theorem. The properties of the Brower modes restict the allowed Liouville theories as follows: For open strings only Liouville theories with a singularity line at one (or both) end of the interval 0 ⩽ σ ⩽ π are allowed. For closed strings no allowed Liouville theory has been found. Liouville theories with periodic boundary conditions are not allowed.