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

TL;DR

This paper investigates a modified closed bosonic string theory with different left and right normal ordering constants, showing it is consistent, ghost-free, and Poincare invariant in 26 dimensions, with a non-trivial massless sector and no tachyons.

Contribution

It demonstrates the self-consistency and physical viability of a closed bosonic string model with asymmetric ordering constants within the old covariant quantization framework.

Findings

Model is ghost free for D=26, a=1, ar a=0.

Absence of tachyons in the spectrum.

Manifest Poincare invariance and non-trivial massless sector.

Abstract

Closed bosonic string with different normal ordering constants $a \ne \bar a$ 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.