Hamiltonian BRST Quantization of the Conformal String

TL;DR

The paper develops a Hamiltonian BRST quantization of the tensionless, conformally invariant string in a $D+2$ dimensional setting and shows that quantum consistency (nilpotency of the BRST charge and Jacobi identities) is achieved only in $D=2$. Using both operator methods with careful regularization and a mode-expansion approach, the authors reveal central extensions in the quantum constraint algebra and demonstrate that a consistent nilpotent BRST charge arises solely at $D=2$. They relate this result to a broader picture in which the theory is topological away from $D=2$ (as in prior work), while in two dimensions it describes massless particles with an infinite-dimensional conformal symmetry. The work emphasizes the critical role of ghosts and regularization in ensuring a well-defined quantum theory and suggests directions for extending the analysis to superstrings and explicit 2D constructions.

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.