Milne Universe, Tachyons, and Quantum Group

TL;DR

This paper investigates the spectrum of strings on a boost orbifold of spacetime, showing that the absence of twisted sector tachyons prevents resolving the cosmological singularity through marginal deformations, and links this to quantum groups.

Contribution

It demonstrates that the twisted sector tachyons are absent in the spectrum due to modular invariance, making the singularity resolution via worldsheet CFT marginal deformations impossible, and connects this to quantum group structures.

Findings

Twisted sector tachyons are absent in the orbifold spectrum.

Resolution of the singularity via marginal deformation is impossible.

Links between Euclidean and Lorentzian orbifolds and quantum groups are established.

Abstract

We analyze the spectrum of the bosonic and superstring on the orbifold of the space-time by a boost, leading to the cosmological singularity. We show that the modular invariance leads to the spectrum where the twisted sector tachyon, together with all other twisted sector fields, present in the Euclidean version of the orbifold, is absent. This makes impossible to resolve the singularity by a marginal deformation of the worldsheet CFT. We also establish a relation between the resolution of rotational orbifolds in Euclidean and Lorentzian setups, and quantum groups. The analysis confirms the impossibility of resolving the cosmological orbifold singularity.