Limiting Cases of a Superstring in ${AdS}_5 \times {S}^5$

The superstring action in ${AdS}_5 \times {S}^5$ depends on two parameters: the inverse string tension $\alpha '$ and the radius $R$. The “standard” AdS/CFT correspondence requires that the string action depend on only the combination $\sqrt \lambda = R^2/\alpha '$. After reviewing previous work on the light-cone superstring, we derive the explicit form of the action $\lambda = 0$. Its zero-mode part coincides with the superparticle action in {${AdS}_5 \times {S}^5$}, and the $\lambda =0$ string spectrum, as expected, must therefore include the “protected” type-IIB supergravity states. Following recent suggestions, we conjecture that such a tensionless string spectrum must also contain higher-spin massless states in $AdS_5$. We also discuss the case of another parameterization of the string action that admits the straightforward flat-space limit $R\to \infty $, but the limits $R \to 0 $ and $\alpha ' \to \infty $ are not equivalent in this case. The limit $R \to 0$ then corresponds to shrinking $S^5$ to the size zero, simultaneously “freezing” the fluctuations of the radial coordinate of $AdS_5$. This case results in a “nonstandard” AdS/CFT correspondence picture.