Tensionless Tales: Vacua and Critical Dimensions

TL;DR

This paper investigates the critical dimensions of three quantum tensionless string theories derived from a classical tensionless string, finding that two are consistent in 26 dimensions while one has no dimension constraint.

Contribution

It performs lightcone quantisation to determine the critical dimensions of three distinct quantum vacua in tensionless string theory, revealing their relation to the standard bosonic string.

Findings

Two vacua are consistent in 26 dimensions.

One vacuum imposes no dimension constraint.

All three are sub-sectors of tensile string theory.

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.