Classical and Quantized Tensionless Strings

TL;DR

This paper derives a geometric action for tensionless strings, explores their symmetries, and quantizes the theory, revealing a potential topological nature with states as diffeomorphism singlets.

Contribution

It introduces a geometric formulation of tensionless strings, analyzes their conformal symmetries, and quantizes the theory while maintaining these symmetries at the quantum level.

Findings

Weyl symmetry is replaced by conformal symmetry in the tensionless limit

Quantization suggests physical states are diffeomorphism singlets

Potential topological nature of the tensionless string theory

Abstract

{}From the ordinary tensile string we derive a geometric action for the tensionless ($T=0$) string and discuss its symmetries and field equations. The Weyl symmetry of the usual string is shown to be replaced by a global space-time conformal symmetry in the $T\to 0$ limit. We present the explicit expressions for the generators of this group in the light-cone gauge. Using these, we quantize the theory in an operator form and require the conformal symmetry to remain a symmetry of the quantum theory. Modulo details concerning zero-modes that are discussed in the paper, this leads to the stringent restriction that the physical states should be singlets under space-time diffeomorphisms, hinting at a topological theory. We present the details of the calculation that leads to this conclusion.