Tensionless Path from Closed to Open Strings

We reconsider the tensionless limit on bosonic closed string theory, where the 3D Bondi-Metzner-Sachs (BMS) algebra appears as symmetries on the world sheet, as opposed to two copies of the Virasoro algebra in the case of the usual tensile theory. This is an ultrarelativistic limit on the world sheet. 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.

Figure 1

Formation of open strings from closed strings.

Figure 2

Formation of space-filling D-brane from closed strings.

Figure 3

Bose-Einstein condensation on the world sheet.