Tensionless Branes and the Null String Critical Dimension

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.

Null branes in string theory backgrounds

“…At the same time, the above equality is the compatibility condition for the solution (12) with the other equations of motion and constraint (10).…”

Tensionless tales: vacua and critical dimensions

“…There are some older papers which have performed BRST quantisation for the tensionless string, e.g. [41,42]. It would be good to re-examine these papers from our recent understanding of the three inequivalent vacua.…”

Low-energy parabosonic membrane: new critical dimensions and deformed noncommutativity

“…A natural way to find a critical dimension for the membrane is to relate this latter to the string theory via dimensional reduction [17]. In this string limit, it is natural to obtain D − 1 = 26 for the bosonic membrane, since one of the D dimension in the membrane is absorbed by the gauge freedom [16,[18][19][20][21][22][23].…”

“…From the P.B (22)(23)(24), one can easily show that the constaints (16)(17)(18) satisfy the following closed algebra…”