Tensionless strings: physical Fock space and higher spin fields

TL;DR

This paper investigates the properties of a tensionless string theory with perimeter action, revealing a 13-dimensional space-time, massless spectrum, and a rich structure of higher spin gauge fields, with implications for understanding higher spin theories.

Contribution

It introduces a new gauge symmetry algebra for tensionless strings and classifies the physical Fock space using the little group E(11), proposing that all excitation levels are null states.

Findings

Space-time must be 13-dimensional for anomaly cancellation.

All particles are massless with no tachyons in the spectrum.

Higher spin gauge fields are realized in the ground state.

Abstract

I study the physical Fock space of the tensionless string theory with perimeter action, exploring its new gauge symmetry algebra. The cancellation of conformal anomaly requires the space-time to be 13-dimensional. All particles are massless and there are no tachyon states in the spectrum. The zero mode conformal operator defines the levels of the physical Fock space. All levels can be classified by the highest Casimir operator W of the little group E(11) for massless particles in 11-dimensions. The ground state is infinitely degenerated and contains massless gauge fields of arbitrary large integer spin, realizing the irreducible representations of E(11) of fixed helicity. The excitation levels realize CSR representations of little group E(11) with an infinite number of helicities. After inspection of the first excitation level, which, as I prove, is a physical null state, I conjecture that all excitation levels are physical null states. In this theory the tensor field of the second rank does not play any distinctive role and therefore one can suggest that in this model there is no gravity.