On consistency of the closed bosonic string with different left-right ordering constants

Closed bosonic string with different normal ordering constants $a\mathrm{\ne }\bar{a}$ for the right and the left moving sectors is considered. One immediate consequence of this choice is absence of tachyon in the physical state spectrum. Selfconsistency of the resulting model in the “old covariant quantization” (OCQ) framework is studyed. The model is manifestly Poincare invariant, it has non trivial massless sector and is ghost free for $D=26, ~ a=1, ~\bar a=0$. A possibility to obtain the light-cone formulation for the model is also discussed.