Tensionless Tales: Vacua and Critical Dimensions

TL;DR

The paper studies the quantum consistency of tensionless bosonic closed strings by performing lightcone quantisation of three vacua that arise from a single ILST-like classical theory. It shows that the Induced vacuum is unconstrained in spacetime dimension, while the Flipped and Oscillator vacua each require $D=26$, indicating these tensionless theories sit inside the usual tensile string theory. The core method is the closure of the Lorentz algebra via $J^{\mu\nu}$ and the analysis of central terms across vacua; the results tie tensionless strings to Ambitwistor-like structures and standard string theory. The findings clarify dimensional ambiguities and guide future work on spectra, BRST quantisation, and tensionless superstrings.

Abstract

Recently, a careful canonical quantisation of the theory of closed bosonic tensionless strings has resulted in the discovery of three separate vacua and hence three different quantum theories that emerge from this single classical tensionless theory. In this note, we perform lightcone quantisation with the aim of determination of the critical dimension of these three inequivalent quantum theories. The satisfying conclusion of a rather long and tedious calculation is that one of vacua does not lead to any constraint on the number of dimensions, while the other two give $D=26$. This implies that all three quantum tensionless theories can be thought of as consistent sub-sectors of quantum tensile bosonic closed string theory.

Figures (1)

• Figure 1: Tensionless corners of Bosonic String Theory.