Tensionless Strings, WZW Models at Critical Level and Massless Higher Spin Fields

TL;DR

The paper investigates the tensionless limit of bosonic string theory across flat and curved target spaces, identifying a critical level where tension vanishes and a large gauge symmetry emerges. By analyzing Virasoro and affine Kac-Moody structures, it shows that in flat space the contracted constraints yield Fronsdal-like equations for free massless higher-spin fields, while in noncompact group manifolds and AdS cosets the tensionless regime arises at a critical level $k$ (e.g., $k=-h^V$ or $k=(d-1)$) with a proliferation of null states signaling enhanced space-time symmetry. However, constructing consistent interacting theories with these higher-spin states remains challenging, and the authors discuss subtleties in the curved backgrounds and potential connections to AdS/CFT, suggesting avenues for extending to supersymmetric cases. Overall, the work proposes a unified view linking tensionless limits to higher-spin dynamics via critical levels in WZW/AdS constructions, while highlighting open questions about interactions and holographic interpretations.

Abstract

We discuss the notion of tensionless limit in quantum bosonic string theory, especially in flat Minkowski space, noncompact group manifolds (e.g., SL(2,R)) and coset manifolds (e.g., AdS). We show that in curved space typically there exists a critical value of the tension which is related to the critical value of the level of the corresponding affine algebra. We argue that at the critical level the sring theory becomes tensionless and that there exists a huge new symmetry of the theory. We dicuss the appearence of the higher spin massless states at the critical level.