On limits of superstring in AdS_5 x S^5

TL;DR

The article investigates the λ→0 (tensionless) limit of the AdS5×S^5 superstring by examining two parameterizations (covariant and light-cone) and deriving explicit λ=0 forms of the action. It shows that the zero-mode sector coincides with the AdS5×S^5 superparticle, naturally containing the protected type IIB supergravity states, and it discusses the potential appearance of higher-spin massless states in AdS5. Through a detailed phase-space, bosonic, and fermionic light-cone analysis, the authors obtain a tensionless limit where certain sectors decouple, while the full supersymmetric background retains nontrivial interactions among the remaining modes. The work highlights how the λ→0 regime provides a concrete framework for exploring higher-spin AdS/CFT and the spectrum of tensionless strings, and it contrasts standard and non-standard parametrizations that yield different continuity properties in the limit.

Abstract

The superstring action in AdS_5 x S^5 depends on two parameters: the inverse string tension a' and the radius R. The standard AdS/CFT correspondence requires that the string coordinates are rescaled so that the action depends only on one combination of the two: (λ)^{1/2} = R^2/a'. Then λ\to 0 limit is equivalent to R \to 0 for fixed $a'$ or to the zero-tension limit in AdS_5 x S^5: a' \to \infty for fixed R. After reviewing previous work hep-th/0009171 on the light cone superstring we explicitly obtain the λ= 0 form of its action. Its zero-mode part is the same as the superparticle action in AdS_5 x S^5, and thus the λ=0 string spectrum must include, as expected, the ``protected'' type IIB supergravity states. Following recent suggestions, it is conjectured that the spectrum of this tensionless string should as well contain higher spin massless states in AdS_5. We also discuss the case of another parametrization of the string action which has straightforward R\to\infty flat space limit but where R \to 0 and a' \to \infty limits are not equivalent. There R \to 0 corresponds to shrinking S^5 to zero the size and ``freezing'' the fluctuations of the radial coordinate of AdS_5. This case is the basis of the ``non-standard'' AdS/CFT correspondence suggested in hep-th/0010106. Parts of this work were presented in the talk at ``Supergravity at 25'' conference, Stony Brook, December 1-2, 2001.