Tensionless branes and the null string critical dimension

TL;DR

This paper investigates the quantization of tensionless p-branes, revealing that the critical dimension depends on operator ordering choices for the null string and that higher-dimensional branes do not impose such restrictions.

Contribution

It extends BRST quantization to tensionless p-branes, analyzing the impact of operator ordering on critical dimensions and proposing a generalization to supersymmetric null branes.

Findings

Critical dimension depends on operator ordering for null strings.

Higher p-branes do not restrict the embedding space-time dimension.

A supersymmetric extension of null branes is proposed.

Abstract

BRST quantization is carried out for a model of p-branes with second class constraints. After extension of the phase space the constraint algebra coincides with the one of null string when p=1. It is shown that in this case one can or can not obtain critical dimension for the null string, depending on the choice of the operator ordering and corresponding vacuum states. When p>1, operator orderings leading to critical dimension in the p=1 case are not allowed. Admissable orderings give no restrictions on the dimension of the embedding space-time. Finally, a generalization to supersymmetric null branes is proposed.