Bosonic string theory with dust

TL;DR

This paper introduces a modified bosonic string theory incorporating a dust field, leading to a natural time gauge and a consistent Fock quantization in lower dimensions, with novel spectra including tachyon-free states.

Contribution

It presents a new bosonic string model with dust, providing a natural gauge, a complete quantization, and novel spectra beyond traditional string theory.

Findings

Fock quantization is complete and consistent for d<26.

The Hamiltonian is not a constraint, allowing new spectra.

Some sectors lack tachyons, unlike standard string theory.

Abstract

We study a modified bosonic string theory that has a pressureless ``dust'' field on the string worldsheet. The dust is a real scalar field with unit gradient which breaks conformal invariance. Hamiltonian analysis reveals a time reparametrization constraint linear in the dust field momentum and a spatial diffeomorphism constraint. This feature provides a natural ``dust time" gauge in analogy with the parametrized particle. In this gauge we give a Fock quantization of the theory, which is complete and self-consistent in d<26. The Hamiltonian of the theory is not a constraint; as a consequence the Hilbert space and mass spectrum are characterized by an additional parameter, and includes the usual string spectrum as a special case. The other sectors provide new particle spectra, some of which do not have tachyons.