Space-Time Symmetries of Quantized Tensionless Strings

TL;DR

The paper addresses the quantum consistency of space-time conformal symmetry in the tensionless string limit $T \to 0$. It uses light-cone quantization and constructs conformal generators to test the full conformal algebra at $\tau=0$, employing a smeared regularization to handle operator products. It finds that the full conformal invariance is anomalous unless the physical Hilbert space is constrained so that states are invariant under general space-time diffeomorphisms (except the centre-of-mass) and that a further condition from $K^-$ enforces masslessness, effectively drastically reducing the spectrum. This points to a framework in which unbroken general covariance and a paucity of short-distance degrees of freedom govern the tensionless regime, with no explicit nontrivial Hilbert space yet provided.

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 Poincaré 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.