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Limiting Cases of a Superstring in ${AdS}_5 \times {S}^5$
A. A. Tseytlinabc a P. N. Lebedev Physical Institute, Russian Academy of Sciences
b Ohio State University
c Imperial College, Theoretical Physics Blackett Laboratory
Abstract:
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.
Keywords:
superstring in the light-cone gauge, low-energy limit, effective action, AdS/CFT correspondence. Received: 07.02.2002
DOI:
10.4213/tmf381
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