On the covariant quantization of tensionless bosonic strings in AdS spacetime

TL;DR

The work investigates covariant quantization of tensionless bosonic strings in AdS, realizing AdS as a hyperboloid in a flat ambient space and analyzing the tensionless limit via constrained Hamiltonian methods. A suitable subset of geometric constraints together with the contracted Virasoro constraints closes to a Lie algebra of first-class constraints, enabling a nilpotent BRST charge that is independent of spacetime dimension. Both open and closed string sectors are treated, yielding explicit covariant BRST charges $Q_{open,AdS}$ and $Q_{closed,AdS}$ that commute with the AdS isometries $SO(2,d-1)$ and do not require a critical dimension. This framework suggests a connection to infinite towers of higher-spin fields on AdS and lays groundwork for interacting tensionless strings and AdS/CFT in the null/tensionless regime via a second-quantized, covariant formalism.

Abstract

The covariant quantization of the tensionless free bosonic (open and closed) strings in AdS spaces is obtained. This is done by representing the AdS space as an hyperboloid in a flat auxiliary space and by studying the resulting string constrained hamiltonian system in the tensionless limit. It turns out that the constraint algebra simplifies in the tensionless case in such a way that the closed BRST quantization can be formulated and the theory admits then an explicit covariant quantization scheme. This holds for any value of the dimension of the AdS space.