Classical and Quantized Tensionless Strings

TL;DR

Isberg, Lindström, Sundborg, and Theodoridis investigate the tensionless limit of the bosonic string by deriving a geometric action that replaces Weyl invariance with space-time conformal symmetry in the T→0 limit. They perform a light-cone quantization and BRST analysis, showing that although the BRST charge can be defined independently of dimension, the quantum realization of conformal symmetry encounters an intrinsic anomaly in the light-cone operator algebra that cannot be canceled by local counterterms under reasonable locality and regularization assumptions. This anomaly imposes strong constraints on physical states, effectively singling out diffeomorphism-invariant states and hinting at a highly topological spectrum. The results support a view of tensionless strings as a topological-like sector of string theory and suggest connections to high-energy/short-distance behavior and possibly non-perturbative dynamics.

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.