Hamiltonian BRST Quantization of the Conformal String

TL;DR

This paper introduces a Hamiltonian BRST quantization of the tensionless conformal string, revealing a critical dimension of 2 and connecting to massless particles and topological phases.

Contribution

It provides a new BRST quantization framework for the conformal string, establishing its critical dimension and clarifying its quantum properties.

Findings

Critical dimension of the conformal string is D=2.

Quantized conformally symmetric tensionless strings describe a topological phase.

The BRST charge's nilpotency ensures consistency and leads to the critical dimension.

Abstract

We present a new formulation of the tensionless string ($T= 0$) where the space-time conformal symmetry is manifest. Using a Hamiltonian BRST scheme we quantize this {\em Conformal String} and find that it has critical dimension $D=2$. This is in keeping with our classical result that the model describes massless particles in this dimension. It is also consistent with our previous results which indicate that quantized conformally symmetric tensionless strings describe a topological phase away {}from $D=2$. We reach our result by demanding nilpotency of the BRST charge and consistency with the Jacobi identities. The derivation is presented in two different ways: in operator language and using mode expansions. Careful attention is payed to regularization, a crucial ingredient in our calculations.