Space-Time Symmetries of Quantized Tensionless Strings

TL;DR

This paper investigates the quantum conformal symmetry of tensionless strings, revealing that full symmetry can be preserved across dimensions only with a significantly reduced spectrum, emphasizing the role of diffeomorphism invariance.

Contribution

It demonstrates that quantum conformal symmetry in tensionless strings can be maintained in any dimension if the spectrum is appropriately reduced, highlighting the importance of symmetry constraints.

Findings

Full conformal symmetry can be preserved in any dimension with spectrum reduction.

Quantum states must be diffeomorphism singlets except for the center of mass.

Spectrum reduction aligns with the zero tension limit of ordinary strings.

Abstract

The tensionless limit of the free bosonic string is space-time conformally symmetric classically. Requiring invariance of the quantum theory in the light cone gauge tests the reparametrization symmetry needed to fix this gauge. The full conformal symmetry gives stronger constraints than the Poincar\'e subalgebra. We find that the symmetry may be preserved in any space-time dimension, but only if the spectrum is drastically reduced (part of this reduction is natural in a zero tension limit of the ordinary string spectrum). The quantum states are required to be symmetric ({\it i.e.} singlets) under space-time diffeomorphisms, except for the centre of mass wave function.