Limiting Cases of a Superstring in AdS5×S5

Abstract

The superstring action in AdS ₅×S ⁵ depends on two parameters: the inverse string tension α′ 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 at λ=0. Its zero-mode part coincides with the superparticle action in AdS ₅×S ⁵, and the λ=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→∞, but the limits R→0 and α′→∞ are not equivalent in this case. The limit R→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.