# The tensionless path from closed to open strings

## TL;DR

This paper explores the tensionless limit of bosonic closed string theory, revealing that open strings emerge from closed strings and that perturbative states condense, linking to long string formation at the Hagedorn temperature.

## Contribution

It demonstrates that in the tensionless limit, the BMS algebra governs the worldsheet symmetries and closed strings transition into open strings via an induced vacuum state.

## Key findings

- Emergence of open strings from closed strings in the tensionless limit.
- Identification of the induced vacuum as a Neumann boundary state.
- Observation of Bose-Einstein-like condensation of perturbative states.

## Abstract

We reconsider the tensionless limit on bosonic closed string theory, where the 3d Bondi-Metzner-Sachs (BMS) algebra appears as symmetries on the worldsheet, as opposed to two copies of the Virasoro algebra in the case of the usual tensile theory. This is an ultra-relativistic limit on the worldsheet. We consider the induced representations of the BMS algebra in the oscillator basis and show that the limit takes the tensile closed string vacuum to the "induced" vacuum which is identified as a Neumann boundary state. Hence, rather remarkably, an open string emerges from closed strings in the tensionless limit. We also follow the perturbative states in the tensile theory in the limit and show that there is a Bose-Einstein like condensation of all perturbative states on this induced vacuum. This ties up nicely with the picture of the formation of a long string from a gas of strings in the Hagedorn temperature, where the effective string tension goes to zero.