A Tale of Three. Tensionless strings and vacuum structure

TL;DR

The paper shows that canonical quantisation of a classical tensionless bosonic string admits three inequivalent quantum theories, corresponding to three distinct tensionless vacua. By analyzing sandwich-type quantum constraints and the resulting BMS3 worldsheet symmetry, it connects the oscillator, induced, and flipped vacua to unique representation structures and central charges, predicting varied spectra and massless towers. The induced vacuum reveals an open-string emergence from a condensation of closed-string DOF, while the flipped vacuum links to highest-weight BMS3 representations and potential ambitwistor-like behavior; the oscillator vacuum hints at a rich higher-spin / gauge structure with null states. Together, these results illuminate the rich algebraic and spectral landscape of tensionless strings and point to future directions in supersymmetric generalisations, BRST quantisation, and nonperturbative worldsheet dynamics.

Abstract

Within the premise of canonical quantisation, we re-examine the quantum structure of bosonic tensionless string theory. In the classical theory, the worldsheet metric degenerates and the Bondi-Metnzer-Sachs (BMS) algebra arises as the residual symmetries on fixing the tensionless equivalent of the conformal gauge. In the quantum regime, we find, on careful examination, that there are multiple ways to impose constraints to restrict the physical Hilbert space, which in turn lead to three distinct choices of tensionless vacua. We analyse these vacua in detail, commenting on various aspects like the central charges and the spectrum around each of them.

Figures (1)

• Figure 1: Mapping of different representations in the singular limits.