String theories with deformed energy momentum relations, and a possible non-tachyonic bosonic string

TL;DR

This paper explores deformed dispersion relations in bosonic string theory, showing that certain models maintain linear propagation and ghost decoupling, while also potentially removing tachyons from the spectrum.

Contribution

It introduces a prescription for deformed dispersion relations in bosonic strings, demonstrating consistent quantization and tachyon elimination in some models.

Findings

String modes propagate with deformed dispersion relations.

Ghost modes can still decouple in these theories.

Some models eliminate the tachyon from the spectrum.

Abstract

We consider a prescription for introducing deformed dispersion relations in the bosonic string action. We find that in a subset of such theories it remains true that the embedding coordinates propagate linearly on the worldsheet. While both the string modes and the center of mass propagate with deformed dispersion relations, the speed of light remains energy independent. We consider the canonical quantization of these strings, and find that it is possible to choose theories so that ghost modes still decouple, as usual. However the Virasoro algebra now exhibits an energy dependent central charge. We also find that there are examples where the tachyon is eliminated from the spectrum of the free bosonic string.